Explanation Given Information: The 17 th term of the sequence a 17 is 25 3 and the 32 th term of the sequence a 32 is 95 6 . Formula used: The n th term of the sequence a n is given by a n = a 1 + ( n − 1 ) d where a 1 is the first term of the sequence, d is the common difference and n is the number of the term. Calculation: Consider the 17 th term a 17 = 25 3 and the 32 th term a 32 = 95 6 . a 17 and a 32 are 15 times apart; 32 − 17 = 15 so add d a total of 15 times to a 17 to get a 32 . a 17 + 15 d = a 32 Substitute the values of a 17 and a 32 a 17 + 15 d = a 32 25 3 + 15 d = 95 6 Add 25 3 on both sides, 25 3 + 15 d = 95 6 25 3 + 15 d − 25 3 = 95 6 − 25 3 15 d = 95 − 50 6 15 d = 45 6 Divide by 15 on both sides: 15 d = 45 6 15 d 15 = 45 6 15 d = 45 3 6 × 15 = 3 6 2 Therefore, the common difference d = 1 2 . Now, a 17 and a 1 are 16 times apart; 17 − 1 = 16 . So, subtract d a total of 16 times from a 17 to get a 1 . a 17 − 16 d = a 1 Substitute the value of d and a 17 in the above equation, a 17 − 16 d = a 1 25 3 − 16 8 ⋅ 1 2 = a 1 25 3 − 8 = a 1 25 − 24 3 = a 1 Solve further, 25 − 24 3 = a 1 1 3 = a 1 Therefore, the first term a 1 = 1 3

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

7th Edition

ISBN: 9780137361847

Author: Marvin Bittinger, David Ellenbogen

Publisher: PEARSON+

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 14.2, Problem 30ES

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To calculate: The value of the first term a1, the common difference d and the first five terms of the arithmetic sequence when the 17^th term of the sequence a17=253 and the 32^th term of the sequence a32=956.

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Chapter 14.2, Problem 29ES

Chapter 14.2, Problem 31ES

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 value of the first term a 1 , the common difference d and the first five terms of the arithmetic sequence when the 17 th term of the sequence a 17 = 25 3 and the 32 th term of the sequence a 32 = 95 6 .

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To calculate: The value of the first term a1, the common difference d and the first five terms of the arithmetic sequence when the 17th term of the sequence a17=253 and the 32th term of the sequence a32=956.

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Chapter 14 Solutions

To calculate: The value of the first term a1, the common difference d and the first five terms of the arithmetic sequence when the 17^th term of the sequence a17=253 and the 32^th term of the sequence a32=956.