Explanation Definition used: Arithmetic: “If the difference between consecutive terms is always the same number, then the sequnce is arithmetic sequence. If the first term is called a 1 and the common difference between the consecutive terms is called d , then the terms the pattern of an arithmetic sequence is a 1 , a 1 + d , a 1 + 2 d , ... ”. Geometric: “If the ratio of consecutive terms in a sequence is constant, then the sequnce is a geometric sequence. If the first term is called a 1 and the common ratio of consecutive terms is called r , then the pattern of a geometric sequence is a 1 , a 1 r , a 1 r 2 , a 1 r 3 , ... ”. Calculation: The given sequence is { a n } = { 4 n ! } . In order to check the difference of any two consecutive terms in a sequence is constant, it is enough to show that a n − a n − 1 is constant. Note that a n and a n − 1 are any two consecutive terms. Substitute n − 1 for n in the sequence a n = 4 n ! to get the value of a n − 1 as follows. a n − 1 = 4 ( n − 1 ) ! Compute the value of a n − a n − 1 . a n − a n − 1 = 4 n ! − 4 ( n − 1 ) ! = 4 ( n − 1 ) ! n ! ( n − 1 ) ! − 4 ( n ! ) n ! ( n − 1 ) ! = 4 ( n − 1 ) ! − 4 ( n ! ) ( n ! ) ( n − 1 ) ! = 4 ( n − 1 ) ! ( 1 − n ) ( n ! ) ( n − 1 ) ! = 4 ( 1 − n ) ( n ! ) Since the difference between the consecutive terms is not constant, the sequence is not arithmetic

3rd Edition

ISBN: 9780321880116

Author: Michael Sullivan III, Katherine R. Struve, Janet Mazzarella

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 13, Problem 3T

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Whether the given sequence is arithmetic, geometric or neither and find the first term a1 and common difference or common ratio if it is arithmetic or geometric.

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Chapter 13, Problem 2T

Chapter 13, Problem 4T

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Ch. 13.1 - A(n) _____ is a function whose domain is the set...Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

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Whether the given sequence is arithmetic, geometric or neither and find the first term a 1 and common difference or common ratio if it is arithmetic or geometric.

Solution Summary: The author explains that the sequence left4n!right is neither arithmetic nor geometric.

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Whether the given sequence is arithmetic, geometric or neither and find the first term a1 and common difference or common ratio if it is arithmetic or geometric.

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Chapter 13 Solutions