Algebra 2 (1st Edition)

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

Chapter 12 Sequences and Series - 12.1 Define and Use Sequences and Series - 12.1 Exercises - Skill Practice - Page 798: 20


n-th term:$\quad a_{n}=\displaystyle \frac{2n}{n+2}$ The next term is $\displaystyle \quad a_{5}=\frac{10}{7}$

Work Step by Step

The n-th numerator is a multiple of 2, starting with $2(1).$ The first denominator is $3 = 2+1$, The 2nd denominator is $4 = 2+2,$ The 3rd denominator is $5 = 2+3,$ $...$ The nth denominator is $2+n$ So, the nth term is $a_{n}=\displaystyle \frac{2n}{n+2}$, and the next term is $a_{5}=\displaystyle \frac{2\cdot 5}{5+2}=\frac{10}{7}$
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