Find the sum of the first n terms of the following arithmetic sequence.
-$$a _ { 2 } = - 65 , a _ { 5 } = 220 ; \mathrm { n } = 10$$
A) 2675
B) $- 5875$
C) 3475
D) $- 3475$

Question

Quizplus · Accepted Answer

The common difference $d$ of the arithmetic sequence can be found using the formula $a_n = a_1 + (n - 1)d$. Given $a_2 = -65$ and $a_5 = 220$, we can set up two equations to solve for $d$ and $a_1$. From $a_5 = a_1 + 4d$, we know $220 = a_1 + 4d$. From $a_2 = a_1 + d$, we know $-65 = a_1 + d$. Solving these equations, we find $d = 95$ and $a_1 = -160$. The sum of the first $n$ terms of an arithmetic sequence is given by $S_n = \frac{n}{2}[2a_1 + (n - 1)d]$. Substituting $n = 10$, $a_1 = -160$, and $d = 95$, we get $S_{10} = \frac{10}{2}[2(-160) + (10 - 1)95] = 5[-320 + 855] = 5 \times 535 = 2675$.

Find the Sum of the First N Terms of the Following