Explanation Given Information: The provided arithmetic series is 1 + 5 + 9 + 13 + ⋯ . Formula used: For any positive integer n ≥ 1 , The sum of first n terms S n of an arithmetic sequence is given by S n = n 2 ( a 1 + a n ) , the n th term a n of the arithmetic sequence is given by a n = a 1 + ( n − 1 ) d and the common difference d is given by d = a n + 1 − a n where a 1 is the first term, a n is the n th term, a n + 1 is the n th term, d is the common difference and n is the number of terms of the arithmetic sequence. Calculation: Consider the arithmetic sequence 1 + 5 + 9 + 13 + ⋯ . The sum of first 20 term S 20 can be calculated by using the formula S n = n 2 ( a 1 + a n ) Here, the first term a 1 = 1 The common difference d can be calculated by using the formula d = a n + 1 − a n for any positive integer n ≥ 1 . For n = 1 , d = a 1 + 1 − a 1 = a 2 − a 1 = 5 − 1 = 4 Now, the 20 th term a 20 is unknown so to find it, use the formula a n = a 1 + ( n − 1 ) d and substitute the values of a 1 = 1 , d = 4 and n = 20 in it

Pearson eText Elementary and Intermediate Algebra: Concepts and Applications -- Instant Access (Pearson+)

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Author: Marvin Bittinger, David Ellenbogen

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Chapter 14.2, Problem 33ES

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To calculate: The sum of first 20 terms of the arithmetic series 1+5+9+13+⋯.

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Chapter 14.2, Problem 32ES

Chapter 14.2, Problem 34ES

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Chapter 14 Solutions

Pearson eText Elementary and Intermediate Algebra: Concepts and Applications -- Instant Access (Pearson+)

Ch. 14.1 - Prob. 1YT Ch. 14.1 - Prob. 2YT Ch. 14.1 - Prob. 3YT Ch. 14.1 - Prob. 4YT Ch. 14.1 - Prob. 5YT Ch. 14.1 - Prob. 1CYU Ch. 14.1 - Prob. 2CYU Ch. 14.1 - Prob. 3CYU Ch. 14.1 - Prob. 4CYU Ch. 14.1 - Prob. 5CYU

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The sum of first 20 terms of the arithmetic series 1 + 5 + 9 + 13 + ⋯ .

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To calculate: The sum of first 20 terms of the arithmetic series 1+5+9+13+⋯.

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Chapter 14 Solutions