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
$$\eqalign{ & = \frac{{{{\left\{ {n\left( {n + 1} \right)} \right\}}^2}}}{4} \cr & \therefore \,{\text{Average}} = \frac{{n{{\left( {n + 1} \right)}^2}}}{4} \cr & \Rightarrow n = 49 \cr & \Rightarrow \frac{{49{{\left( {50} \right)}^2}}}{4} = 30625 \cr} $$