Find the sum,m, $\mathrm { s } _ { \mathbf { n } },$ , o f the sequence.
-15, 6, -3, -12, . . ., -156
A)-165
B)-1410
C)-1500
D)-1404

Question

Quizplus · Accepted Answer

The sequence is an arithmetic sequence with the first term $a = 15$ and common difference $d = 6 - 15 = -9$. The last term is $-156$. Using the formula for the nth term of an arithmetic sequence, $a_n = a + (n-1)d$, we find $n$. Solving $-156 = 15 + (n-1)(-9)$ gives $n = 20$. The sum of an arithmetic sequence is given by $S_n = \frac{n}{2} (a + a_n)$. Substituting the values, $S_{20} = \frac{20}{2} (15 - 156) = 10 \times (-141) = -1410$.

Find the Sum,m sn,\mathrm { s } _ { \mathbf { n } },sn​,

Find the Sum,m $\mathrm { s } _ { \mathbf { n } },$