The arithmetic mean of 1, 8, 27, 64,………..up to an terms is given by

Options

A. `(n(n+1))/(2)`
B. `(n(n+1)^(2))/(2)`
C. `(n(n+1)^(2))/(4)`
D. `(n^(2)(n+1)^(2))/(4)`

Answer

C

Explanation

Sum of the given terms `=1+8+27+64……….+"upto n terms"`
`"Sum "=1^(3)+2^(3)+3^(3)+4^(3)+……….+" upto n terms"`
`"Sum "=((n(n+1))/(2))^(2)=(n^(2)(n+a)^(2))/(4)`
`AM=(n^(2)(n+1)^(2))/(4)xx(1)/(n)=(n(n+1)^(2))/(4)`