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Questions and Answers
What is the sum of the first 10 terms of the AP: 2, 7, 12, ... ?
What is the sum of the first 10 terms of the AP: 2, 7, 12, ... ?
What is the value of 'n' and 'an' in the AP with a = 2, d = 8, and Sn = 90?
What is the value of 'n' and 'an' in the AP with a = 2, d = 8, and Sn = 90?
What is the value of 'n' and 'a' in the AP with an = 4, d = 2, and Sn = -14?
What is the value of 'n' and 'a' in the AP with an = 4, d = 2, and Sn = -14?
The value of 'd' in an arithmetic progression represents the common difference between the terms.
The value of 'd' in an arithmetic progression represents the common difference between the terms.
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An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is the same.
An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is the same.
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The sum of an arithmetic progression can be calculated using the formula Sn = n/2(2a + (n-1)d), where Sn represents the sum of the first 'n' terms, 'a' represents the first term, and 'd' represents the common difference.
The sum of an arithmetic progression can be calculated using the formula Sn = n/2(2a + (n-1)d), where Sn represents the sum of the first 'n' terms, 'a' represents the first term, and 'd' represents the common difference.
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Study Notes
Arithmetic Progression (AP) Basics
- An arithmetic progression is a sequence where the difference between consecutive terms is constant, referred to as the common difference (d).
- The first term of an AP is denoted as 'a'.
Sum of the First n Terms
- The sum of the first 'n' terms (Sn) can be calculated using:
( S_n = \frac{n}{2} (2a + (n-1)d) )
where:- ( S_n ) = sum of the first n terms
- ( a ) = first term
- ( d ) = common difference
- ( n ) = number of terms
Calculation Examples
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For the AP: 2, 7, 12, ... (where a = 2, d = 5):
- The first 10 terms sum up to:
( S_{10} = \frac{10}{2} (2 \times 2 + (10 - 1) \times 5) = 5 (4 + 45) = 5 \times 49 = 245 )
- The first 10 terms sum up to:
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Given values: a = 2, d = 8, and ( S_n = 90 ):
- Using the sum formula to find 'n' and ( a_n ):
- Substitute known values into the formula and solve for 'n'.
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Given values: ( a_n = 4 ), d = 2, and ( S_n = -14 ):
- Use the known parameters to derive 'n' and the first term 'a'.
- Set up equations based on the sum formula and solve accordingly.
Key Concepts
- ( d ) (common difference) is crucial for determining the progression of terms in an AP.
- Understanding how to manipulate the sum formula is essential for solving problems related to arithmetic progressions.
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Description
Challenge yourself with this quiz on arithmetic progressions! Test your skills in finding the sum of APs, calculating the nth term and solving for missing values. Put your mathematical abilities to the test with various problems ranging from finding the sum of multiples to solving for the value of 'n'. Sharpen your problem-solving skills and boost your confidence in APs with this quiz.
