Question

If the sum of $n$ terms of the series $2^3+4^3+$ $6^3$ + ... is 3528, then $n$ equals to :

• A. 10
• B. 7
• C. 8
• D. 9
• E. 6

Answer 1

Answer: (E)

Given series is $2^3+4^3+6^3+...$
$\therefore$ $T_n={(2n)}^3=8n^3$
$\therefore$ $\Sigma T_n=8\Sigma n^3=\frac{8n^2{(n+1)}^2}{4}$
$\Rightarrow$ $3528=2n^2{(n+1)}^2$ (given)
$\Rightarrow$ $n=6$