Question

The 4^th and the 7^th terms of a G.P. are `1/27` and `1/729` respectively. Find the sum of n terms of this G.P.

Answer 1

For a G.P.,

4^th term = ar³ = `1/27`

7^th term = ar⁶ = `1/729`

Now, `(ar^6)/(ar^3) = (1/729)/(1/27)`

`=> r^3 = 1/27 = (1/3)^3`

`=> r = 1/3`  ...(∵ r < 1)

`=> a xx 1/27 = 1/27`

`=>` a = 1

`S_n = (a(1 - r^n))/(1 - r)`

`=> S_n = (1(1 - (1/3)^n))/(1 - 1/3)`

= `(1 - 1/3^n)/(2/3)`

= `3/2(1 - 1/3^n)`