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 5 th term is –2 and 13 th term is –30, that is, a 5 = − 2 , a 13 = 30 . The common difference is calculated as follows. Substitute n = 5 in a n = a 1 + ( n − 1 ) d . a 5 = a 1 + ( 5 − 1 ) d a 5 = a 1 + 4 d Thus, a 1 + 4 d = − 2 (1) Substitute n = 13 in a n = a 1 + ( n − 1 ) d . a 13 = a 1 + ( 13 − 1 ) d a 13 = a 1 + 12 d Thus, a 1 + 12 d = 30 (2) Subtract equation (2) from equation (1). a 1 + 4 d = − 2 a 1 + 12 d = 30 _ 0 − 8 d = − 32 8 d = 32 d = 4 Thus d = 4

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Chapter 13.2, Problem 36AYU

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The first term and the common difference of the arithmetic sequence whose 5^th term is –2 and the 13^th term is 30; give a recursive formula for the sequence and find the nth term of that sequence.

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Chapter 13.2, Problem 35AYU

Chapter 13.2, Problem 37AYU

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Chapter 13 Solutions

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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 5 th term is –2 and the 13 th term is 30; 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 5th term is –2 and the 13th term is 30; 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 5^th term is –2 and the 13^th term is 30; give a recursive formula for the sequence and find the nth term of that sequence.