Question

find the sum, $s_n$, for the arithmetic series described? remember to use the formula $s_n = \frac{n}{2}(a_1 + a_n)$ where $a_1 = 12$, $a_n = 75$, $n = 13$. \\(\circ\\) a. $s_{13}=1053$ \\(\circ\\) b. $s_{13}=565.5$ \\(\circ\\) c. $s_{13}=409.5$ \\(\circ\\) d. $s_{13}=1131$

Explanation:

Step1: Substitute values into formula

Substitute $a_1=12$, $a_n=75$, $n=13$ into $S_n=\frac{n}{2}(a_1+a_n)$:
$$S_{13}=\frac{13}{2}(12+75)$$

Step2: Calculate sum inside parentheses

Compute $12+75$:
$$12+75=87$$

Step3: Compute final sum

Multiply $\frac{13}{2}$ by 87:
$$S_{13}=\frac{13\times87}{2}=\frac{1131}{2}=565.5$$

Answer:

b. $S_{13}=565.5$