Question

For the G.P. `1/27, 1/9, 1/3, ........., 81`; find the product of fourth term from the beginning and the fourth term from the end.

Answer 1

Given G.P. : `1/27, 1/9, 1/3, ........., 81` 

Here,
Common ratio, r = `(1/9)/(1/27)` = 3

First term, a = `1/27` and last term, l = 81

∴ 4^th term from the beginning = ar³

= `1/27 xx (3)^3`

= `1/27 xx 27`

= 1

And 4^th term from an end = `1/r^3`

= `81/(3)^3`

= `81/27`

= 3

Thus, required product = 1 × 3 = 3