Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 12 Sequences and Series - Mixed Review of Problem Solving - Lessons 12.1-12.3 - Page 818: 8


The geometric series is: $1,2, 4,8,16$. The arithmetic series is: $0,3.1, 6.2, 9.3, 12.4$

Work Step by Step

Consider the geometric series $1,2, 4,8,16$. This shows that the sum is $31$. The general formula for the sum of the nth term of an arithmetic series is given by $S_n= \dfrac{n}{2}(a_1+a_n)$ We know that $a_n=a_1+(n-1)d$ Thus, $S_n= \dfrac{n}{2}(2a_1+(n-1)d)$ $31= \dfrac{5}{2}(2(0)+(5-1)d)$ This gives: $d=\dfrac{31}{10}=3.1$ Thus, we have the arithmetic series: $0,3.1, 6.2, 9.3, 12.4$
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