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: 26


n-th term:$\quad a_{n}=1.2+7.8n$, The next term is $\quad a_{5}=40.2$

Work Step by Step

Note that $16.8-9=7.8,$ $24.6-16.8=7.8,$ $32.4-24.6=7.8$ .... and we can also rewrite the first term as $1.2+7.8$ (to fit the pattern) $n=1,\quad 9=1.2+7.8$ $n=2,\quad 16.8=9+7.8\quad=1.2+2\times 7.8$ $n=3,\quad 24.6=16.8+7.8=1.2+3\times 7.8$ $n=4,\quad 32.4=24.6+7.8=1.2+4\times 7.8\quad...$ So, the nth term is $a_{n}=1.2+n\times 7.8$, and the next term is $a_{5}=32.4+7.8=40.2$ (also, $1.2+5\times 7.8=40.2$ )
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