Find the average of cubes of first 49 positive integers.

A. 30625

B. 1225

C. 30125

D. 6235

Answer: Option A

Solution(By Examveda Team)

Sum of cubes of first n positive consecutive numbers is $$ = \frac{{{{\left( {n\left( {n + 1} \right)} \right)}^2}}}{4}$$
Average
$$ = \frac{{{{\left( {n\left( {n + 1} \right)} \right)}^2}}}{4}$$
$$\eqalign{ & \Rightarrow n = 49 \cr & \Rightarrow \frac{{49{{\left( {50} \right)}^2}}}{4} \cr & \Rightarrow 30625 \cr} $$