Question

value: 3
evaluate
\\(\displaystyle\sum_{n = 1}^{7} (9n + 5)\\)
\\(\circ\\) a. \\(s_n = 574\\)
\\(\circ\\) b. \\(s_n = 189\\)
\\(\circ\\) c. \\(s_n = 525\\)
\\(\circ\\) d. \\(s_n = 287\\)

Explanation:

Step1: Split the summation

$\sum_{n=1}^{7} (9n + 5) = 9\sum_{n=1}^{7}n + \sum_{n=1}^{7}5$

Step2: Compute sum of first 7 integers

Use formula $\sum_{n=1}^{k}n = \frac{k(k+1)}{2}$.
$\sum_{n=1}^{7}n = \frac{7(7+1)}{2} = 28$

Step3: Compute sum of constant term

$\sum_{n=1}^{7}5 = 5\times7 = 35$

Step4: Substitute back and calculate

$9\times28 + 35 = 252 + 35$

Answer:

d. $S_n$=287