In a geometric progression with first term a and common ratio r, what is the arithmetic mean of first five terms?

Options

A. `a+2r`
B. `ar^(2)`
C. `a(r^(5)-1)//(r-1)`
D. `a(r^(5)-1)//[5(r-1)]`

Answer

D

Explanation

Let the Geometric progression be `a,ar,ar^(2),ar^(3),ar^(4)…` First five terms of a geometric progression are `a,ar,ar^(2),ar^(3),ar^(4).`
`:." ""Mean"=(a+ar+ar^(2)+ar^(3)+ar^(4))/(5)`
`=(a(r^(5)-1))/(5(r-1))" "(because" Sum of G.P."=(a(r^(n)-1))/(r-1))`