Question

Find the number of terms in the following G.P.

`1/3, 1/9, 1/27, ..., 1/2187`

Answer 1

`1/3, 1/9, 1/27, ..., 1/2187`

Hint:
3	729
3	243
3	81
3	27
3	9
3	3
	1

Here a = `1/3`, r = `(1/9)/(1/3)`

= `1/9 xx 3/1`

= `1/3`

t_n = ar^n–1

`1/3 xx (1/3)^("n" - 1)`

= `1/2817`

`(1/3)^("n" - 1) = 1/2817 xx 3`

= `1/729`

`(1/3)^("n" - 1) = 1/3^6`

= `(1/3)^6`

n – 1 = 6

n = 6 + 1 = 7

∴ No. of terms = 7