Explanation Given information : The give sequence is − 3 , 5 4 , − 7 9 , 9 16 , − 11 25 , … Method used : The formula for general term of a sequence is obtained by observing the pattern of occurring of consecutive terms. Calculations: The given sequence is − 3 , 5 4 , − 7 9 , 9 16 , − 11 25 , … ... (1) In the sequence (1) we observe three patterns; (i) The terms occurring in sequence are alternately as − , + , − , + , , so the formula for this pattern is ( − 1 ) n , n ∈ ℕ . (ii) The terms occurring in numerator of the consecutive terms of sequence are alternately 3 , 5 , 7 , 9 , 11 , that is an arithmetic sequence with first term a = 3 and common difference d = + 2 so the formula for this pattern is T n = a + ( n − 1 ) d = 3 + ( n − 1 ) 2 = 2 n + 1 , n ∈ ℕ . (iii) The terms occurring in denominator of the consecutive terms of sequence are alternately 1 , 4 , 9 , 16 , 25 , so the formula for this pattern is T n = 1 n 2 , n ∈ ℕ

15th Edition

ISBN: 9781305420878

Author: Stewart

Publisher: CENGAGE L

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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 1, Problem 38E

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Tofind:The formula for the general term of given sequence.

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Tofind: The formula for the general term of given sequence.

Solution Summary: The author explains how the formula for general term of a sequence is obtained by observing the pattern of occurring of consecutive terms.

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Chapter 1 Solutions