Explanation Definition used: Arithmetic sequence : An arithmetic sequence may be defined recursively as a 1 = a , a n − a n − 1 = d or as a 1 = a , a n = a n − 1 + d . Where a 1 = a and d are real numbers. The number a is the first term, and the number d is called the common difference. The terms of an arithmetic sequence with first term a 1 and common difference d are a 1 , a 1 + d , a 1 + 2 d , a 1 + 3 d , … . Theorem used: The n t h term of an arithmetic sequence: For an arithmetic sequence { a n } whose first term is a 1 and whose common difference is d , the n t h term is determined by the formula a n = a 1 + ( n − 1 ) d . Calculation: Given arithmetic sequence 9 th term is –5 and 15 th term is 31, that is, a 9 = − 5 , a 15 = 31 . The common difference is calculated as follows. Substitute n = 9 in a n = a 1 + ( n − 1 ) d . a 9 = a 1 + ( 9 − 1 ) d a 9 = a 1 + 8 d Thus, a 1 + 8 d = − 5 (1) Substitute n = 15 in a n = a 1 + ( n − 1 ) d . a 15 = a 1 + ( 15 − 1 ) d a 15 = a 1 + 14 d Thus, a 1 + 14 d = 31 (2) Subtract equation (2) from equation (1). a 1 + 8 d = − 5 a 1 + 14 d = 31 _ 0 − 6 d = − 36 6 d = 36 d = 6 Thus d = 6

11th Edition

ISBN: 9780135163078

Author: Michael Sullivan

Publisher: PEARSON

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Chapter 13.2, Problem 33AYU

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The first term and the common difference of the arithmetic sequence whose 9^th term is –5 and the 15^th term is 31; give a recursive formula for the sequence and find the nth term of that sequence.

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Chapter 13.2, Problem 32AYU

Chapter 13.2, Problem 34AYU

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Chapter 13 Solutions

Algebra And Trigonometry (11th Edition)

Ch. 13.1 - Prob. 1AYU Ch. 13.1 - Prob. 2AYU Ch. 13.1 - Prob. 3AYU Ch. 13.1 - Prob. 4AYU Ch. 13.1 - Prob. 5AYU Ch. 13.1 - Prob. 6AYU Ch. 13.1 - Prob. 7AYU Ch. 13.1 - Prob. 8AYU Ch. 13.1 - Prob. 9AYU Ch. 13.1 - Prob. 10AYU

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The first term and the common difference of the arithmetic sequence whose 9 th term is –5 and the 15 th term is 31; give a recursive formula for the sequence and find the n t h term of that sequence.

The first term and the common difference of the arithmetic sequence whose 9th term is –5 and the 15th term is 31; give a recursive formula for the sequence and find the nth term of that sequence.

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Chapter 13 Solutions

The first term and the common difference of the arithmetic sequence whose 9^th term is –5 and the 15^th term is 31; give a recursive formula for the sequence and find the nth term of that sequence.