(a) Explanation It is given that the first term is 59,049 and the common difference is − 1 3 . So, a 1 = a = 59 , 049 . a 2 = a r = 59 , 049 × − 1 3 = − 19,683 . a 3 = a r 2 = 59 , 049 × ( − 1 3 ) 2 = 59 , 049 × 1 9 = 6 , 561 . a 4 = a r 3 = 59 , 049 × ( − 1 3 ) 3 = 59 , 049 × − 1 27 = − 2 , 187 . a 5 = a r 4 = 59 , 049 × ( − 1 3 ) 4 = 59 , 049 × 1 81 = 729 . a 6 = a r 5 = 59 , 049 × ( − 1 3 ) 5 = 59 , 049 × − 1 243 = − 243 . a 7 = a r 6 = 59 , 049 × ( − 1 3 ) 6 = 59 , 049 × 1 729 = 81 . a 8 = a r 7 = 59 , 049 × ( − 1 3 ) 7 = 59 , 049 × − 1 2187 = − 27 (b) To determine The sum of the first 12 terms of thegeometric sequence with first term 59,049 and common ratio − 1 3 .

Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)

3rd Edition

ISBN: 9780134689555

Author: Edgar Goodaire, Michael Parmenter

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 5.2, Problem 25E

(a)

To determine

The first ten terms and the 33^rd term of thegeometric sequence with first term 59,049 and common ratio −13.

(b)

To determine

The sum of the first 12 terms of thegeometric sequence with first term 59,049 and common ratio −13.

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Chapter 5.2, Problem 24E

Chapter 5.2, Problem 26E

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Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)

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The first ten terms and the 33 rd term of thegeometric sequence with first term 59,049 and common ratio − 1 3 .

Solution Summary: The author determines the first ten terms and the 33 rd term of thegeometric sequence with first term 59,049 and common ratio -13.

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The first ten terms and the 33^rd term of thegeometric sequence with first term 59,049 and common ratio −13.

The sum of the first 12 terms of thegeometric sequence with first term 59,049 and common ratio −13.

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Chapter 5 Solutions

The first ten terms and the 33 rd term of thegeometric sequence with first term 59,049 and common ratio − 1 3 .

Solution Summary: The author determines the first ten terms and the 33 rd term of thegeometric sequence with first term 59,049 and common ratio -13.

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The first ten terms and the 33rd term of thegeometric sequence with first term 59,049 and common ratio −13.

The sum of the first 12 terms of thegeometric sequence with first term 59,049 and common ratio −13.

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Chapter 5 Solutions

The first ten terms and the 33^rd term of thegeometric sequence with first term 59,049 and common ratio −13.