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

Sum $= - 3230$

Explanation:

Given first term ${a}_{1} = 137$
common difference $= - 12$

number of terms $n = 38$

compute the 38th term
${a}_{38} = {a}_{1} + \left(n - 1\right) \cdot d$

${a}_{38} = 137 + \left(38 - 1\right) \cdot \left(- 12\right)$

${a}_{38} = - 307$

Compute sum ${S}_{38}$

${S}_{38} = \frac{n}{2} \cdot \left({a}_{1} + {a}_{38}\right)$

${S}_{38} = \frac{38}{2} \cdot \left(137 + \left(- 307\right)\right)$

${S}_{38} = - 3230$

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