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

1 Answer
Feb 23, 2018

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= 27/64or

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