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Questions and Answers
What are the next two terms in the sequence: -8, -5, -2, 1, 4, 7,...?
What are the next two terms in the sequence: -8, -5, -2, 1, 4, 7,...?
7, 10
What are the next two terms in the sequence: 1, 4, 9, 16, 25, 36,...?
What are the next two terms in the sequence: 1, 4, 9, 16, 25, 36,...?
49, 64
What are the next two terms in the sequence: 0.1, 0.01, 0.001, 0.0001,...?
What are the next two terms in the sequence: 0.1, 0.01, 0.001, 0.0001,...?
0.00001, 0.000001
What are the next two terms in the sequence: 1, 2, 3, 3, 4, 4,...?
What are the next two terms in the sequence: 1, 2, 3, 3, 4, 4,...?
What is the first term and common difference of the following arithmetic progression: 8 + 11 + 14 + 17 + ...?
What is the first term and common difference of the following arithmetic progression: 8 + 11 + 14 + 17 + ...?
What is the first term and common difference of the following arithmetic progression: 23 + 25 + 27 + 29 + ...?
What is the first term and common difference of the following arithmetic progression: 23 + 25 + 27 + 29 + ...?
What is the first term and common difference of the following arithmetic progression: 19 + 16 + 13 + 10 + ...?
What is the first term and common difference of the following arithmetic progression: 19 + 16 + 13 + 10 + ...?
What is the first term and common difference of the following arithmetic progression: 13 + 15 + 16 + 18 + ...?
What is the first term and common difference of the following arithmetic progression: 13 + 15 + 16 + 18 + ...?
What is the first term and common difference of the following arithmetic progression: -11.5 - 9 - 6.5 - 4 - ...?
What is the first term and common difference of the following arithmetic progression: -11.5 - 9 - 6.5 - 4 - ...?
What is the first term and common difference of the following arithmetic progression: 6 + 6 + 7 + 7 + ...?
What is the first term and common difference of the following arithmetic progression: 6 + 6 + 7 + 7 + ...?
What is the first term and common difference of the following arithmetic progression: -8 - 7 - 6 - 5 - ...?
What is the first term and common difference of the following arithmetic progression: -8 - 7 - 6 - 5 - ...?
What is the first term and common difference of the following arithmetic progression: 6 + 3 + 0 - 3 - ...?
What is the first term and common difference of the following arithmetic progression: 6 + 3 + 0 - 3 - ...?
How many terms are there in the following arithmetic progression: 5 + 8 + 11 + 14 + ... + 59 + 62?
How many terms are there in the following arithmetic progression: 5 + 8 + 11 + 14 + ... + 59 + 62?
How many terms are there in the following arithmetic progression: 1 + 6 + 11 + 16 + ... + 501 + 506?
How many terms are there in the following arithmetic progression: 1 + 6 + 11 + 16 + ... + 501 + 506?
How many terms are there in the following arithmetic progression: -193 - 189 - 185 - ... - 21 - 17?
How many terms are there in the following arithmetic progression: -193 - 189 - 185 - ... - 21 - 17?
How many terms are there in the following arithmetic progression: 2 + 17 + 32 + ... + 20 + 20 + 20?
How many terms are there in the following arithmetic progression: 2 + 17 + 32 + ... + 20 + 20 + 20?
What is the 18th term of a series that has the nth term given by 2 + 3n?
What is the 18th term of a series that has the nth term given by 2 + 3n?
What is the 31st term of a series that has the nth term given by (10 + 2n)?
What is the 31st term of a series that has the nth term given by (10 + 2n)?
What is the 50th term of a series that has the nth term given by (32 - n)?
What is the 50th term of a series that has the nth term given by (32 - n)?
What are the 6th and 7th terms of a series that has the nth term given by (-1)^(2n+1)?
What are the 6th and 7th terms of a series that has the nth term given by (-1)^(2n+1)?
Find an expression for the nth term of the arithmetic progression: 5 + 8 + 11 + 14 + ... and use it to write down the 100th term of the series.
Find an expression for the nth term of the arithmetic progression: 5 + 8 + 11 + 14 + ... and use it to write down the 100th term of the series.
Find an expression for the nth term of the arithmetic progression: 5 + 2 - 1 - 4 - ... and use it to write down the 100th term of the series.
Find an expression for the nth term of the arithmetic progression: 5 + 2 - 1 - 4 - ... and use it to write down the 100th term of the series.
Find an expression for the nth term of the arithmetic progression: 12 + 16 + 19 + 23 + ... and use it to write down the 100th term of the series.
Find an expression for the nth term of the arithmetic progression: 12 + 16 + 19 + 23 + ... and use it to write down the 100th term of the series.
For the arithmetic progression: 7 + 12 + 17 + 22 + 27 + ..., which is the first term to exceed 1000?
For the arithmetic progression: 7 + 12 + 17 + 22 + 27 + ..., which is the first term to exceed 1000?
For the arithmetic progression: -24 - 21.5 - 19 - 16.5 - 14 - ..., which is the first term to be negative?
For the arithmetic progression: -24 - 21.5 - 19 - 16.5 - 14 - ..., which is the first term to be negative?
For the arithmetic progression: 843 + 836 + 829 + 822 + ..., which is the first term to be negative?
For the arithmetic progression: 843 + 836 + 829 + 822 + ..., which is the first term to be negative?
For the arithmetic progression: 56.3 + 55.4 + 54.5 + 53.6 + ..., which is the first term to be negative?
For the arithmetic progression: 56.3 + 55.4 + 54.5 + 53.6 + ..., which is the first term to be negative?
What are the values of a and d in the arithmetic progression 2 + 6 + 10 + 14 + ..., and what is S₁₂?
What are the values of a and d in the arithmetic progression 2 + 6 + 10 + 14 + ..., and what is S₁₂?
What are the values of a and d in the arithmetic progression 10 + 8 + 6 + 4 + ..., and what is S₁₅?
What are the values of a and d in the arithmetic progression 10 + 8 + 6 + 4 + ..., and what is S₁₅?
What are the values of a and d in the arithmetic progression 4.5 + 6 + 7.5 + 9 + ..., and what is S₁₉?
What are the values of a and d in the arithmetic progression 4.5 + 6 + 7.5 + 9 + ..., and what is S₁₉?
What are the values of a and d in the arithmetic progression 15 + 13 + 11 + 9 + ..., and what is S₁₆?
What are the values of a and d in the arithmetic progression 15 + 13 + 11 + 9 + ..., and what is S₁₆?
What are the values of a and d in the arithmetic progression 7 + 3 - 1 - 5 - ..., and what is S₂₀?
What are the values of a and d in the arithmetic progression 7 + 3 - 1 - 5 - ..., and what is S₂₀?
What are the values of a and d in the arithmetic progression 1 - 6 - 5 - 3 - 2 - 1/2 ..., and what is S₁₂?
What are the values of a and d in the arithmetic progression 1 - 6 - 5 - 3 - 2 - 1/2 ..., and what is S₁₂?
What are the values of a and d in the arithmetic progression -9 - 7 - 5 - 3 - ..., and what is S₁₆?
What are the values of a and d in the arithmetic progression -9 - 7 - 5 - 3 - ..., and what is S₁₆?
What is the sum of the arithmetic progression: 2 + 4 + 6 + 8 + ... + 146?
What is the sum of the arithmetic progression: 2 + 4 + 6 + 8 + ... + 146?
What is the sum of the arithmetic progression: 100 + 95 + 90 + 85 + 80 + ... -20?
What is the sum of the arithmetic progression: 100 + 95 + 90 + 85 + 80 + ... -20?
What is the sum of the arithmetic progression: 4 + 10 + 16 + 22 + 28 + ... + 334?
What is the sum of the arithmetic progression: 4 + 10 + 16 + 22 + 28 + ... + 334?
What is the sum of the arithmetic progression: 51 + 41 + 33 + ... -3?
What is the sum of the arithmetic progression: 51 + 41 + 33 + ... -3?
In an arithmetic progression, u₅ = 8 and u₈ = 14; find a, d, and S₁₀.
In an arithmetic progression, u₅ = 8 and u₈ = 14; find a, d, and S₁₀.
In an arithmetic progression, u₃ = 7.5 and u₁₀ = 11; find a, d, and S₈.
In an arithmetic progression, u₃ = 7.5 and u₁₀ = 11; find a, d, and S₈.
In an arithmetic progression, u₁ = 15 and u₈ = 7; find a, d, and S₂₂.
In an arithmetic progression, u₁ = 15 and u₈ = 7; find a, d, and S₂₂.
In an arithmetic progression, u₃ = -4 and u₈ = 8; find a, d, and S₉.
In an arithmetic progression, u₃ = -4 and u₈ = 8; find a, d, and S₉.
In an arithmetic progression, u₂ = -12 and S₁₂ = 18; find a, d, and u₆.
In an arithmetic progression, u₂ = -12 and S₁₂ = 18; find a, d, and u₆.
In an arithmetic progression, u₅ = -0.5 and S₇ = 21; find a, d, and u₉.
In an arithmetic progression, u₅ = -0.5 and S₇ = 21; find a, d, and u₉.
In an arithmetic progression, u₁₅ = 7 and S₉ = 18; find a, d, and u₂₀.
In an arithmetic progression, u₁₅ = 7 and S₉ = 18; find a, d, and u₂₀.
The sum of the first 10 terms of an arithmetic progression is 120 and the sum of the first 20 terms is 840. Find the sum of the first 30 terms.
The sum of the first 10 terms of an arithmetic progression is 120 and the sum of the first 20 terms is 840. Find the sum of the first 30 terms.
An arithmetic progression has a common difference 'd'. If the sum to 20 terms is 25 times the first term, find, in terms of 'd', the sum to 30 terms.
An arithmetic progression has a common difference 'd'. If the sum to 20 terms is 25 times the first term, find, in terms of 'd', the sum to 30 terms.
In an arithmetic progression, a = -23 and d = 2.5; find the least value of 'n' such that Sₙ > 0.
In an arithmetic progression, a = -23 and d = 2.5; find the least value of 'n' such that Sₙ > 0.
In an arithmetic progression, a = -61 and d = 4; find the least value of 'n' such that Sₙ > 0.
In an arithmetic progression, a = -61 and d = 4; find the least value of 'n' such that Sₙ > 0.
An arithmetic progression has a first term of 10 and a common difference of 0.25. Find the least number of terms the arithmetic progression can have, given that the number of terms exceeds 300.
An arithmetic progression has a first term of 10 and a common difference of 0.25. Find the least number of terms the arithmetic progression can have, given that the number of terms exceeds 300.
An arithmetic progression has a first term of -5 and a common difference of 1.5. Find the greatest number of terms the arithmetic progression can have, given that the sum of the terms does not exceed 450.
An arithmetic progression has a first term of -5 and a common difference of 1.5. Find the greatest number of terms the arithmetic progression can have, given that the sum of the terms does not exceed 450.
The sum to 'n' terms of a particular series is given by Sₙ = 17n - 3n². Find an expression for the sum to (n-1) terms.
The sum to 'n' terms of a particular series is given by Sₙ = 17n - 3n². Find an expression for the sum to (n-1) terms.
The sum to 'n' terms of a particular series is given by Sₙ = 17n - 3n². Find an expression for the nth term of the series.
The sum to 'n' terms of a particular series is given by Sₙ = 17n - 3n². Find an expression for the nth term of the series.
The sum to 'n' terms of a particular series is given by Sₙ = 17n - 3n². Show that the series is an arithmetic progression and find the first term and common difference.
The sum to 'n' terms of a particular series is given by Sₙ = 17n - 3n². Show that the series is an arithmetic progression and find the first term and common difference.
Three consecutive terms of an arithmetic progression have a sum of 36 and a product of 1428. Find the three terms.
Three consecutive terms of an arithmetic progression have a sum of 36 and a product of 1428. Find the three terms.
A particular arithmetic progression has a positive common difference and is such that for any three adjacent terms, three times the sum of their squares exceeds the square of their sum by 37.5. Find the common difference.
A particular arithmetic progression has a positive common difference and is such that for any three adjacent terms, three times the sum of their squares exceeds the square of their sum by 37.5. Find the common difference.
Find the common difference, the nth term, and the sum to n terms of the following arithmetic progression: ln 3 + ln 3² + ln 3³ + ln 3⁴ + ...
Find the common difference, the nth term, and the sum to n terms of the following arithmetic progression: ln 3 + ln 3² + ln 3³ + ln 3⁴ + ...
Find expressions for the nth term and the sum to 'n' terms of the arithmetic progression: ln(ab) + ln(ab²) + ln(ab³) + ln(ab⁴) + ...
Find expressions for the nth term and the sum to 'n' terms of the arithmetic progression: ln(ab) + ln(ab²) + ln(ab³) + ln(ab⁴) + ...
What are the next two terms of the following sequence: -8, -5, -2, 1, 4, 7, ...?
What are the next two terms of the following sequence: -8, -5, -2, 1, 4, 7, ...?
What are the next two terms of the following sequence: 1, 4, 9, 16, 25, 36, ...?
What are the next two terms of the following sequence: 1, 4, 9, 16, 25, 36, ...?
What are the next two terms of the following sequence: 0.1, 0.01, 0.001, 0.0001, ...?
What are the next two terms of the following sequence: 0.1, 0.01, 0.001, 0.0001, ...?
What are the next two terms of the following sequence: 1, 2, 3, 3, 4, ...?
What are the next two terms of the following sequence: 1, 2, 3, 3, 4, ...?
What is the first term and common difference of the arithmetic progression (A.P.): 8 + 11 + 14 + 17 + ...?
What is the first term and common difference of the arithmetic progression (A.P.): 8 + 11 + 14 + 17 + ...?
What is the first term and common difference of the arithmetic progression (A.P.): 23 + 25 + 27 + 29 + ...?
What is the first term and common difference of the arithmetic progression (A.P.): 23 + 25 + 27 + 29 + ...?
What is the first term and common difference of the arithmetic progression (A.P.): 19 + 16 + 13 + 10 + ...?
What is the first term and common difference of the arithmetic progression (A.P.): 19 + 16 + 13 + 10 + ...?
What is the first term and common difference of the arithmetic progression (A.P.): 13 + 15 + 16 + 18 + ...?
What is the first term and common difference of the arithmetic progression (A.P.): 13 + 15 + 16 + 18 + ...?
What is the first term and common difference of the arithmetic progression (A.P.): -11.5 - 9 - 6.5 - 4 - ...?
What is the first term and common difference of the arithmetic progression (A.P.): -11.5 - 9 - 6.5 - 4 - ...?
What is the first term and common difference of the arithmetic progression (A.P.): 6 + 6 + 7 + 7 + ...?
What is the first term and common difference of the arithmetic progression (A.P.): 6 + 6 + 7 + 7 + ...?
What is the first term and common difference of the arithmetic progression (A.P.): -8 - 7 - 6 - 5 - ...?
What is the first term and common difference of the arithmetic progression (A.P.): -8 - 7 - 6 - 5 - ...?
What is the first term and common difference of the arithmetic progression (A.P.): 6 + 3 + 0 - 3 - ...?
What is the first term and common difference of the arithmetic progression (A.P.): 6 + 3 + 0 - 3 - ...?
How many terms are in the arithmetic progression (A.P.): 5 + 8 + 11 + 14 + ... + 59 + 62?
How many terms are in the arithmetic progression (A.P.): 5 + 8 + 11 + 14 + ... + 59 + 62?
How many terms are in the arithmetic progression (A.P.): 1 + 6 + 11 + 16 + ... + 501 + 506?
How many terms are in the arithmetic progression (A.P.): 1 + 6 + 11 + 16 + ... + 501 + 506?
How many terms are in the arithmetic progression (A.P.): -193 - 189 - 185 - ... - 21 - 17?
How many terms are in the arithmetic progression (A.P.): -193 - 189 - 185 - ... - 21 - 17?
Which term in the arithmetic progression (A.P.): 7 + 12 + 17 + 22 + 27 + ... is the first to exceed 1000?
Which term in the arithmetic progression (A.P.): 7 + 12 + 17 + 22 + 27 + ... is the first to exceed 1000?
Which term in the arithmetic progression (A.P.): -24 - 21.5 - 19 - 16.5 - 14 - ... is the first to be negative?
Which term in the arithmetic progression (A.P.): -24 - 21.5 - 19 - 16.5 - 14 - ... is the first to be negative?
Which term in the arithmetic progression (A.P.): 843 + 836 + 829 + 822 + ... is the first to be negative?
Which term in the arithmetic progression (A.P.): 843 + 836 + 829 + 822 + ... is the first to be negative?
Which term in the arithmetic progression (A.P.): 56.3 + 55.4 + 54.5 + 53.6 + ... is the first to be negative?
Which term in the arithmetic progression (A.P.): 56.3 + 55.4 + 54.5 + 53.6 + ... is the first to be negative?
What are the values of a and d in the arithmetic progression (A.P.): 2 + 6 + 10 + 14 + ... and find S₁₂?
What are the values of a and d in the arithmetic progression (A.P.): 2 + 6 + 10 + 14 + ... and find S₁₂?
What are the values of a and d in the arithmetic progression (A.P.): 10 + 8 + 6 + 4 + ... and find S₁₅?
What are the values of a and d in the arithmetic progression (A.P.): 10 + 8 + 6 + 4 + ... and find S₁₅?
What are the values of a and d in the arithmetic progression (A.P.): 4.5 + 6 + 7.5 + 9 + ... and find S₁₉?
What are the values of a and d in the arithmetic progression (A.P.): 4.5 + 6 + 7.5 + 9 + ... and find S₁₉?
What are the values of a and d in the arithmetic progression (A.P.): 15 + 13 + 11 + 9 + ... and find S₁₆?
What are the values of a and d in the arithmetic progression (A.P.): 15 + 13 + 11 + 9 + ... and find S₁₆?
What are the values of a and d in the arithmetic progression (A.P.): 7 + 3 - 1 - 5 - ... and find S₂₀?
What are the values of a and d in the arithmetic progression (A.P.): 7 + 3 - 1 - 5 - ... and find S₂₀?
What are the values of a and d in the arithmetic progression (A.P.): 1 - 6 - 5 - 3 - 2 - 1/2 and find S₁₆?
What are the values of a and d in the arithmetic progression (A.P.): 1 - 6 - 5 - 3 - 2 - 1/2 and find S₁₆?
What are the values of a and d in the arithmetic progression (A.P.): -9 - 7 - 5 - 3 - ... and find S₁₆?
What are the values of a and d in the arithmetic progression (A.P.): -9 - 7 - 5 - 3 - ... and find S₁₆?
Flashcards
Sequence 1
Sequence 1
The sequence is -8, -5, -2, 1, 4, 7...
Sequence 2
Sequence 2
The sequence is 1, 4, 9, 16, 25, 36...
Sequence 3
Sequence 3
The sequence is 0.1, 0.01, 0.001, 0.0001...
Sequence 4
Sequence 4
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Arithmetic Progression (A.P) definition
Arithmetic Progression (A.P) definition
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Finding the first term of an A.P.
Finding the first term of an A.P.
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Common difference of an A.P.
Common difference of an A.P.
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Finding the nth term of a sequence
Finding the nth term of a sequence
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Find the number of terms in an A.P.
Find the number of terms in an A.P.
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Sum of an Arithmetic Progression
Sum of an Arithmetic Progression
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Arithmetic Progression
Arithmetic Progression
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Common Difference
Common Difference
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First Term
First Term
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nth term
nth term
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Study Notes
Arithmetic Progressions - Exercise
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Find the next two terms: Various sequences are given. Students need to determine the pattern (arithmetic or other) and calculate the next two terms. Examples include: -8,-5,-2,1,4,7...; 1,4,9,16,25,36...; 0.1,0.01,0.001,0.0001...; 1,2,3,3,4...
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Find the first term and common difference: Given arithmetic progressions (A.P.s), students must identify the first term (a) and the common difference (d). Examples from the provided exercises include: 8+11+14+17+... , 23+25+27+29+... , 19+16+13+10+..., etc.
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Find the number of terms: Students must determine the total number of terms in A.P.s. Examples include: 5+8+11+14+...+59+62; 1+6+11+16+...+501+506; -193-189-185-...-21-17
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Find specific terms (e.g., 18th, 31st, 50th): Calculate specific terms of A.P.s given the nth term formula.
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Find the nth term: Given formulas for the nth term, find specific terms (e.g., 6th, 7th).
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Find sum of A.P series: Students compute the sums of various arithmetic progressions, with varying formulas and conditions. Examples include finding the sum of the first 10, 20, or 30 terms of an A.P.
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State values of 'a' and 'd' in A.P.s: Various arithmetic progressions are provided, and students must state values for 'a' (first term) and 'd' (common difference) to determine the sum up to specific terms (e.g., S₁₂).
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Find sum of terms of certain A.P series: Specific A.P. series are given and students must calculate the sum of terms up to a specified term (or n).
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Finding terms that exceed a certain value: Identify the earliest term in a series that exceeds a specified value (usually 1000).
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Find the first negative term in an A.P.: Identify the term which is the first to be negative in the provided sequences.
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Understanding the expression for the sum of specified terms and the nth term.
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Finding common difference and the related expressions
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Given the sum to n terms, finding nth terms and understanding various concepts: A variety of problems based on different conditions related to Arithmetic Progressions. Examples include finding the sum of x terms, finding specific terms given sums etc.
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Description
Test your understanding of arithmetic progressions through a variety of exercises. This quiz includes finding the next terms in sequences, identifying the first term and common difference, determining the total number of terms, and calculating specific terms. Challenge yourself with these engaging problems that will reinforce your skills in A.P.s.
