Question

How do you write the expression for the nth term of the geometric sequence `a_1=16, a_4=27/4, n=3`?

Answer 1

`n` th term is `a_1*r^(n-1)` and `a_3=16`

Explanation:

In Geometric progression `n` th term is `a_1*r^(n-1)` where

`a_1` is first term and `r` is the common ratio.

`a_1=16 , a_4=27/4`

`:. a_4=16*r^(4-1) or a_4= 16r^3 = 27/4 or r^3= 27/64`or

`r= root(3)(27/64)=3/4`. When `n=3 :. a_3= 16* (3/4)^(3-1)`

or `a_3= 16* (3/4)^(3-1)=16*(3/4)^2=9`