# Chapter 8, Sequences and Series - Section 8.2 - Arithmetic Sequences - 8.2 Exercises: 54

$S_{25}=6850$

#### Work Step by Step

RECALL: The sum of the first $n$ terms ($S_n$) of an arithmetic sequence is given by the formula: $S_n=\dfrac{n}{2}\left[2a+(n-1)d\right]$ where $a$ = first term $d$ = common difference The given arithmetic sequence has: $a=-2 \\d=23$ Thus, to find the sum of the first 25 terms, substitute the given values to the formula above to obtain: $S_n=\dfrac{n}{2}[2a+(n-1)d] \\S_{25}=\dfrac{25}{2}[2(-2) + (25-1)(23)] \\S_{25}=\dfrac{25}{2}[-4+24(23)] \\S_{25}=\dfrac{25}{2}(-4+552) \\S_{25}=\dfrac{25}{2}(548) \\S_{25}=6850$

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