solve:-
Here,
a₅ = ar⁴ = 512 .............. 1
and,
a₉ = ar⁸ = 131072 .............. 2

Dividing equation (2) by (1), we get.

[ar⁸]/[ar⁴] = [131072]/[512]
=> r⁴ = 256
=> r⁴ = 4⁴
=> r = 4

Equation (1) we get
ar⁴ = 512
=> a4⁴ = 512
=> a * 256 = 512
=> a = 512 / 256
=> a = 2
ie. a = 2 and r = 4

Now,
Here, first term = 2,
common ratio = 4
then,
14^th term is = 2*4 ^{(14 - 1)}
= 2*4 ¹³
= 2*67108864
=> 14^th term is = 134217728