The second term of a Gp is 4 the fifth term is 81 .find the seventh term

3 answers

A5/A2 = ar^4 / ar = r^3 = 81/4
Now solve for a and r, and then find A7 = ar^6
I suspect a typo.
The second term of a Gp is 4 ---> ar = 4
the fifth term is 81 ---> ar^4 = 81
divide them:
r^3 = 81/4 or 162/8
r = 162^(1/3) / 2

seventh term = ar^6 = ar^4 ( r^2)
= 81(162^(2/3)/4

Are you sure you don't have a typo?
e.g. If instead of r^3 = 81/4 , we would have had r^2= 81/4
this would have worked out so much nicer
There's not a typo please