Question

The n^th term of a progression is `3^(n + 1)`. Show that it is a G.P. Also, find its 5th term.

Answer 1

n^th term = `3^(n + 1)`

1^st term = `3^(1 + 1)`

= 3²

= 9

2^nd term = `3^(2 + 1)`

= 3³

= 27

`(a_2)/(a_1) = 27/9`

= 3

If we are getting a constant common ratio, then this series is a GP.

5^th term = `3^(5 + 1)`

= 3⁶

= 729