Question

evaluate
\\(\displaystyle\sum_{n=1}^{5} (7n - 3)\\)
\\(\text{a. } s_n = 170\\)
\\(\text{b. } s_n = 70\\)
\\(\text{c. } s_n = 180\\)
\\(\text{d. } s_n = 90\\)

Explanation:

Step1: Expand the summation

$\sum_{n=1}^{5} (7n-3) = (7(1)-3)+(7(2)-3)+(7(3)-3)+(7(4)-3)+(7(5)-3)$

Step2: Calculate each term

$=(7-3)+(14-3)+(21-3)+(28-3)+(35-3) = 4+11+18+25+32$

Step3: Sum the terms

$4+11+18+25+32 = 90$

Answer:

d. $S_n=90$