Question

What is the sum of the series (image below)

a. 1,830
b. 2,010
c. 5,400
d. 5,490

Answer 1

The answer is D) 5,490.

Explanation:

Answer 2

d. 5490

Explanation:

`\begin{aligned}\displaystyle \sf \sum_(n=1)^(60) 3n & =3(1)+3(2)+3(3)+...+3(49)+3(50)\\ & = 3+6+9+...+147+150\end{aligned}`

Therefore, this is an arithmetic series with:

• first term (a) = 3
• common difference (d) = 3

Sum of the first n terms of an arithmetic series:

`S_n=\frac12n[2a+(n-1)d]`

Therefore, the sum of the first 60 terms:

`\begin{aligned}S_(60) &=\frac12(60)[2(3)+(60-1)3]\\ & =30[6+(59)3]\\ & = 30[6+177]\\ & = 30[183]\\ & = 5490 \end{aligned}`