Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 9 - Sequences and Series - 9-4 Arithmetic Series - Practice and Problem-Solving Exercises - Page 591: 23

Answer

$S_{8} = 20$

Work Step by Step

In order to find the sum of this finite series, we need to find the first term, $a_{1}$ and the last term, $a_{8}$. First, use the explicit formula given and plug in $1$ for $n$ to find $a_{1}$: $a_{1} = 7 - 1$ Subtract: $a_{1} = 6$ Use the explicit formula and plug in $8$ for $n$ to find $a_{8}$: $a_{8} = 7 - 8$ Subtract: $a_{8} = -1$ Plug the two values just found into the formula for the sum of a finite arithmetic series, which is given by $S_{n} = \frac{n}{2}(a_{1} + a_{n})$, to find the sum of the series: $S_{8} = \frac{8}{2}(6 + (-1))$ Evaluate what is inside the parentheses first: $S_{8} = \frac{8}{2}(5)$ Multiply: $S_{8} = \frac{40}{2}$ Simplify the fraction: $S_{8} = 20$
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