Find the indicated partial sum for the given sequence with the given first term and general term.
-$s _ { 6 } , a _ { 1 } = 8 , a _ { n } = a _ { n } - 1 - 5$
A) $- 27$
B) $- 49$
C) $- 35$
D) $- 10$

Question

Quizplus · Accepted Answer

The sequence is arithmetic with the first term $a_1 = 8$ and common difference $d = -5$. The nth term of an arithmetic sequence is given by $a_n = a_1 + (n - 1)d$. The sum of the first n terms, $s_n$, of an arithmetic sequence is given by $s_n = \frac{n}{2}[2a_1 + (n - 1)d]$. For $s_6$, $n = 6$, $a_1 = 8$, and $d = -5$, so $s_6 = \frac{6}{2}[2(8) + (6 - 1)(-5)] = 3[16 - 25] = 3(-9) = -27$.

Find the Indicated Partial Sum for the Given Sequence with the Given