What is the sum of the arithmetic sequence 137, 125, 113 …, if there are 38 terms?

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Answer 1 · 2016-05-15T12:09:13

Sum $= - 3230$ $=-3230$

Given first term $a_{1} = 137$ $a_1=137$
common difference $= - 12$ $=-12$

number of terms $n = 38$ $n=38$

compute the 38th term
$a_{38} = a_{1} + (n - 1) \cdot d$ $a_38=a_1+(n-1)*d$

$a_{38} = 137 + (38 - 1) \cdot (- 12)$ $a_38=137+(38-1)*(-12)$

$a_{38} = - 307$ $a_38=-307$

Compute sum $S_{38}$ $S_38$

$S_{38} = \frac{n}{2} \cdot (a_{1} + a_{38})$ $S_38=n/2*(a_1+a_38)$

$S_{38} = \frac{38}{2} \cdot (137 + (- 307))$ $S_38=38/2*(137+(-307))$

$S_{38} = - 3230$ $S_38=-3230$

God bless...I hope the explanation is useful.