Arithmetic Progressions - Exercise
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Questions and Answers

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,...?

49, 64

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,...?

<p>5, 5</p> Signup and view all the answers

What is the first term and common difference of the following arithmetic progression: 8 + 11 + 14 + 17 + ...?

<p>First term: 8, Common difference: 3</p> Signup and view all the answers

What is the first term and common difference of the following arithmetic progression: 23 + 25 + 27 + 29 + ...?

<p>First term: 23, Common difference: 2</p> Signup and view all the answers

What is the first term and common difference of the following arithmetic progression: 19 + 16 + 13 + 10 + ...?

<p>First term: 19, Common difference: -3</p> Signup and view all the answers

What is the first term and common difference of the following arithmetic progression: 13 + 15 + 16 + 18 + ...?

<p>First term: 13, Common difference: 2</p> Signup and view all the answers

What is the first term and common difference of the following arithmetic progression: -11.5 - 9 - 6.5 - 4 - ...?

<p>First term: -11.5, Common difference: 2.5</p> Signup and view all the answers

What is the first term and common difference of the following arithmetic progression: 6 + 6 + 7 + 7 + ...?

<p>First term: 6, Common difference: 1</p> Signup and view all the answers

What is the first term and common difference of the following arithmetic progression: -8 - 7 - 6 - 5 - ...?

<p>First term: -8, Common difference: 1</p> Signup and view all the answers

What is the first term and common difference of the following arithmetic progression: 6 + 3 + 0 - 3 - ...?

<p>First term: 6, Common difference: -3</p> Signup and view all the answers

How many terms are there in the following arithmetic progression: 5 + 8 + 11 + 14 + ... + 59 + 62?

<p>13</p> Signup and view all the answers

How many terms are there in the following arithmetic progression: 1 + 6 + 11 + 16 + ... + 501 + 506?

<p>102</p> Signup and view all the answers

How many terms are there in the following arithmetic progression: -193 - 189 - 185 - ... - 21 - 17?

<p>46</p> Signup and view all the answers

How many terms are there in the following arithmetic progression: 2 + 17 + 32 + ... + 20 + 20 + 20?

<p>20</p> Signup and view all the answers

What is the 18th term of a series that has the nth term given by 2 + 3n?

<p>56</p> Signup and view all the answers

What is the 31st term of a series that has the nth term given by (10 + 2n)?

<p>72</p> Signup and view all the answers

What is the 50th term of a series that has the nth term given by (32 - n)?

<p>-18</p> Signup and view all the answers

What are the 6th and 7th terms of a series that has the nth term given by (-1)^(2n+1)?

<p>6th term: 1, 7th term: -1</p> Signup and view all the answers

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.

<p>nth term: 3n + 2, 100th term: 302</p> Signup and view all the answers

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.

<p>nth term: 8 - 3n, 100th term: -292</p> Signup and view all the answers

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.

<p>nth term: 7 + 4n, 100th term: 407</p> Signup and view all the answers

For the arithmetic progression: 7 + 12 + 17 + 22 + 27 + ..., which is the first term to exceed 1000?

<p>202nd term</p> Signup and view all the answers

For the arithmetic progression: -24 - 21.5 - 19 - 16.5 - 14 - ..., which is the first term to be negative?

<p>The first term is already negative, but the term -24 is the first term that exceeds 1000.</p> Signup and view all the answers

For the arithmetic progression: 843 + 836 + 829 + 822 + ..., which is the first term to be negative?

<p>The 122nd term</p> Signup and view all the answers

For the arithmetic progression: 56.3 + 55.4 + 54.5 + 53.6 + ..., which is the first term to be negative?

<p>The 63rd term</p> Signup and view all the answers

What are the values of a and d in the arithmetic progression 2 + 6 + 10 + 14 + ..., and what is S₁₂?

<p>a = 2, d = 4, S₁₂ = 294</p> Signup and view all the answers

What are the values of a and d in the arithmetic progression 10 + 8 + 6 + 4 + ..., and what is S₁₅?

<p>a = 10, d = -2, S₁₅ = 0</p> Signup and view all the answers

What are the values of a and d in the arithmetic progression 4.5 + 6 + 7.5 + 9 + ..., and what is S₁₉?

<p>a = 4.5, d = 1.5, S₁₉ = 220.5</p> Signup and view all the answers

What are the values of a and d in the arithmetic progression 15 + 13 + 11 + 9 + ..., and what is S₁₆?

<p>a = 15, d = -2, S₁₆ = 0</p> Signup and view all the answers

What are the values of a and d in the arithmetic progression 7 + 3 - 1 - 5 - ..., and what is S₂₀?

<p>a = 7, d = -4, S₂₀ = -260</p> Signup and view all the answers

What are the values of a and d in the arithmetic progression 1 - 6 - 5 - 3 - 2 - 1/2 ..., and what is S₁₂?

<p>a = 1, d = -7, S₁₂ = -414</p> Signup and view all the answers

What are the values of a and d in the arithmetic progression -9 - 7 - 5 - 3 - ..., and what is S₁₆?

<p>a = -9, d = 2, S₁₆ = 16</p> Signup and view all the answers

What is the sum of the arithmetic progression: 2 + 4 + 6 + 8 + ... + 146?

<p>5336</p> Signup and view all the answers

What is the sum of the arithmetic progression: 100 + 95 + 90 + 85 + 80 + ... -20?

<p>630</p> Signup and view all the answers

What is the sum of the arithmetic progression: 4 + 10 + 16 + 22 + 28 + ... + 334?

<p>8550</p> Signup and view all the answers

What is the sum of the arithmetic progression: 51 + 41 + 33 + ... -3?

<p>656</p> Signup and view all the answers

In an arithmetic progression, u₅ = 8 and u₈ = 14; find a, d, and S₁₀.

<p>a = 2, d = 2, S₁₀ = 100</p> Signup and view all the answers

In an arithmetic progression, u₃ = 7.5 and u₁₀ = 11; find a, d, and S₈.

<p>a = 5, d = 0.5, S₈ = 40</p> Signup and view all the answers

In an arithmetic progression, u₁ = 15 and u₈ = 7; find a, d, and S₂₂.

<p>a = 15, d = -1, S₂₂ = -110</p> Signup and view all the answers

In an arithmetic progression, u₃ = -4 and u₈ = 8; find a, d, and S₉.

<p>a = -13, d = 2, S₉ = 0</p> Signup and view all the answers

In an arithmetic progression, u₂ = -12 and S₁₂ = 18; find a, d, and u₆.

<p>a = -10, d = 2, u₆ = 2</p> Signup and view all the answers

In an arithmetic progression, u₅ = -0.5 and S₇ = 21; find a, d, and u₉.

<p>a = 2, d = -1, u₉ = -6</p> Signup and view all the answers

In an arithmetic progression, u₁₅ = 7 and S₉ = 18; find a, d, and u₂₀.

<p>a = 21, d = -2, u₂₀ = -27</p> Signup and view all the answers

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.

<p>2520</p> Signup and view all the answers

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.

<p>Sum of 30 terms: 75a + 375d</p> Signup and view all the answers

In an arithmetic progression, a = -23 and d = 2.5; find the least value of 'n' such that Sₙ > 0.

<p>n ≥ 10</p> Signup and view all the answers

In an arithmetic progression, a = -61 and d = 4; find the least value of 'n' such that Sₙ > 0.

<p>n ≥ 16</p> Signup and view all the answers

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.

<p>301</p> Signup and view all the answers

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.

<p>19</p> Signup and view all the answers

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.

<p>Sₙ₋₁ = 17(n-1) - 3(n-1)²</p> Signup and view all the answers

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.

<p>aₙ = 17 - 6n</p> Signup and view all the answers

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.

<p>The series is an arithmetic progression with a first term of 14 and a common difference of -6.</p> Signup and view all the answers

Three consecutive terms of an arithmetic progression have a sum of 36 and a product of 1428. Find the three terms.

<p>The three terms are 6, 12, and 18.</p> Signup and view all the answers

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.

<p>The common difference is 2.5</p> Signup and view all the answers

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 + ...

<p>Common difference: ln 3, nth term: ln 3ⁿ, Sum to n terms: (n/2)(ln 3 + ln 3ⁿ)</p> Signup and view all the answers

Find expressions for the nth term and the sum to 'n' terms of the arithmetic progression: ln(ab) + ln(ab²) + ln(ab³) + ln(ab⁴) + ...

<p>nth term: ln(abⁿ), Sum to n terms: (n/2)(ln(ab) + ln(abⁿ))</p> Signup and view all the answers

What are the next two terms of the following sequence: -8, -5, -2, 1, 4, 7, ...?

<p>7, 10</p> Signup and view all the answers

What are the next two terms of the following sequence: 1, 4, 9, 16, 25, 36, ...?

<p>49, 64</p> Signup and view all the answers

What are the next two terms of the following sequence: 0.1, 0.01, 0.001, 0.0001, ...?

<p>0.00001, 0.000001</p> Signup and view all the answers

What are the next two terms of the following sequence: 1, 2, 3, 3, 4, ...?

<p>4, 5</p> Signup and view all the answers

What is the first term and common difference of the arithmetic progression (A.P.): 8 + 11 + 14 + 17 + ...?

<p>First term = 8, Common difference = 3</p> Signup and view all the answers

What is the first term and common difference of the arithmetic progression (A.P.): 23 + 25 + 27 + 29 + ...?

<p>First term = 23, Common difference = 2</p> Signup and view all the answers

What is the first term and common difference of the arithmetic progression (A.P.): 19 + 16 + 13 + 10 + ...?

<p>First term = 19, Common difference = -3</p> Signup and view all the answers

What is the first term and common difference of the arithmetic progression (A.P.): 13 + 15 + 16 + 18 + ...?

<p>First term = 13, Common difference = 2.5</p> Signup and view all the answers

What is the first term and common difference of the arithmetic progression (A.P.): -11.5 - 9 - 6.5 - 4 - ...?

<p>First term = -11.5, Common difference = 2.5</p> Signup and view all the answers

What is the first term and common difference of the arithmetic progression (A.P.): 6 + 6 + 7 + 7 + ...?

<p>First term = 6, Common difference = 1/2</p> Signup and view all the answers

What is the first term and common difference of the arithmetic progression (A.P.): -8 - 7 - 6 - 5 - ...?

<p>First term = -8, Common difference = 1</p> Signup and view all the answers

What is the first term and common difference of the arithmetic progression (A.P.): 6 + 3 + 0 - 3 - ...?

<p>First term = 6, Common difference = -3</p> Signup and view all the answers

How many terms are in the arithmetic progression (A.P.): 5 + 8 + 11 + 14 + ... + 59 + 62?

<p>17</p> Signup and view all the answers

How many terms are in the arithmetic progression (A.P.): 1 + 6 + 11 + 16 + ... + 501 + 506?

<p>102</p> Signup and view all the answers

How many terms are in the arithmetic progression (A.P.): -193 - 189 - 185 - ... - 21 - 17?

<p>46</p> Signup and view all the answers

Which term in the arithmetic progression (A.P.): 7 + 12 + 17 + 22 + 27 + ... is the first to exceed 1000?

<p>201st term</p> Signup and view all the answers

Which term in the arithmetic progression (A.P.): -24 - 21.5 - 19 - 16.5 - 14 - ... is the first to be negative?

<p>The 1st term</p> Signup and view all the answers

Which term in the arithmetic progression (A.P.): 843 + 836 + 829 + 822 + ... is the first to be negative?

<p>122nd term</p> Signup and view all the answers

Which term in the arithmetic progression (A.P.): 56.3 + 55.4 + 54.5 + 53.6 + ... is the first to be negative?

<p>57th term</p> Signup and view all the answers

What are the values of a and d in the arithmetic progression (A.P.): 2 + 6 + 10 + 14 + ... and find S₁₂?

<p>a = 2, d = 4, S₁₂ = 288</p> Signup and view all the answers

What are the values of a and d in the arithmetic progression (A.P.): 10 + 8 + 6 + 4 + ... and find S₁₅?

<p>a = 10, d = -2, S₁₅ = 0</p> Signup and view all the answers

What are the values of a and d in the arithmetic progression (A.P.): 4.5 + 6 + 7.5 + 9 + ... and find S₁₉?

<p>a = 4.5, d = 1.5, S₁₉ = 220.5</p> Signup and view all the answers

What are the values of a and d in the arithmetic progression (A.P.): 15 + 13 + 11 + 9 + ... and find S₁₆?

<p>a = 15, d = -2, S₁₆ = 0</p> Signup and view all the answers

What are the values of a and d in the arithmetic progression (A.P.): 7 + 3 - 1 - 5 - ... and find S₂₀?

<p>a = 7, d = -4, S₂₀ = -260</p> Signup and view all the answers

What are the values of a and d in the arithmetic progression (A.P.): 1 - 6 - 5 - 3 - 2 - 1/2 and find S₁₆?

<p>a = 1, d = -7, S₁₆ = -528</p> Signup and view all the answers

What are the values of a and d in the arithmetic progression (A.P.): -9 - 7 - 5 - 3 - ... and find S₁₆?

<p>a = -9, d = 2, S₁₆ = 80</p> Signup and view all the answers

Study Notes

Arithmetic Progressions - Exercise

  • 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...

  • 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.

  • 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

  • Find specific terms (e.g., 18th, 31st, 50th): Calculate specific terms of A.P.s given the nth term formula.

  • Find the nth term: Given formulas for the nth term, find specific terms (e.g., 6th, 7th).

  • 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.

  • 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).

  • 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).

  • Finding terms that exceed a certain value: Identify the earliest term in a series that exceeds a specified value (usually 1000).

  • Find the first negative term in an A.P.: Identify the term which is the first to be negative in the provided sequences.

  • Understanding the expression for the sum of specified terms and the nth term.

  • Finding common difference and the related expressions

  • 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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Related Documents

Series 1 Arithmetic Progressions Exercise PDF
Series 3 Exercise PDF

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.

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