Explanation Given information: Sequence, { − 1 2 ⋅ 4 n } . Explanation: Consider the sequence, { − 1 2 ⋅ 4 n } . n th term of the sequence is a n = − 1 2 ⋅ 4 n and (n-1) th term is a n − 1 = − 1 2 ⋅ 4 n − 1 Let’s check if the ratio of consecutive terms is constant. a n a n − 1 = − 1 2 ⋅ 4 n − 1 2 ⋅ 4 n − 1 = − 1 2 ⋅ 4 n − 1 ⋅ 4 − 1 2 ⋅ 4 n − 1 = 4 The ratio of consecutive terms is constant; hence the sequence is geometric with common ratio r = 4

10th Edition

ISBN: 8220101460912

Author: Sullivan

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 12, Problem 7CT

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Whether the sequence {−12⋅4n} is arithmetic, geometric, or neither. If the sequence is arithmetic find the common difference and the sum of the first n terms. If the sequence is geometric find the common ratio and sum of the first n terms.

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Chapter 12, Problem 6CT

Chapter 12, Problem 8CT

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Whether the sequence { − 1 2 ⋅ 4 n } is arithmetic, geometric, or neither. If the sequence is arithmetic find the common difference and the sum of the first n terms. If the sequence is geometric find the common ratio and sum of the first n terms.

Solution Summary: The author analyzes whether the sequence left-12cdot4nright is arithmetic, geometric, or neither.