Explanation Given information: The arithmetic sequence is 13 3 , 19 3 , 25 3 , … , 73 3 . Formula used: The n th term of an arithmetic sequence is, a n = a 1 + ( n − 1 ) d Where, a n is the n th term, a 1 is the first term, n is the number of term and d is the common difference. The value of common difference is, d = a 2 − a 1 Where, a 2 is the second term. The distributive property is a ( b + c ) = a b + a c . Calculation: Consider the arithmetic sequence 13 3 , 19 3 , 25 3 , … , 73 3 . The first term a 1 is 13 3 , the second term a 2 is 19 3 and the n th term a n is 73 3 . Substitute a 1 = 13 3 and a 2 = 19 3 in d = a 2 − a 1 to calculate the value of d . d = 19 3 − 13 3 = 19 − 13 3 = 6 3 = 2 The value of common difference d is 2

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ISBN: 9781264367702

Author: Miller

Publisher: MCGRAW-HILL HIGHER EDUCATION

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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 14.3, Problem 49PE

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To calculate: The number of terms in the arithmetic sequence 133,193,253,…,733.

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Chapter 14.3, Problem 48PE

Chapter 14.3, Problem 50PE

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Chapter 14 Solutions

BEGINNING AND INTERMEDIATE AGEBRA

Ch. 14.1 - Prob. 1SP Ch. 14.1 - Prob. 2SP Ch. 14.1 - Evaluate the expressions. 3. 1! Ch. 14.1 - Prob. 4SP Ch. 14.1 - Prob. 5SP Ch. 14.1 - Prob. 6SP Ch. 14.1 - Write out the first three terms of ( x + y ) 5 .Ch. 14.1 - 8. Use the binomial theorem to expand . Ch. 14.1 - Use the binomial theorem to expand ( 2 a − 3 b 2 )...Ch. 14.1 - Find the fourth term of ( x + y ) 8 .

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The number of terms in the arithmetic sequence 13 3 , 19 3 , 25 3 , … , 73 3 .

Solution Summary: The author calculates the number of terms in the arithmetic sequence 133,.

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Chapter 14 Solutions