solve:-
Here,
a₆ = ar⁵ = 6144 .............. 1
and,
a₁₀ = ar⁹ = 1572864 .............. 2

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

[ar⁹]/[ar⁵] = [1572864]/[6144]
=> r⁴ = 256
=> r⁴ = 4⁴
=> r = 4

Equation (1) we get
ar⁵ = 6144
=> a4⁵ = 6144
=> a * 1024 = 6144
=> a = 6144 / 1024
=> a = 6
ie. a = 6 and r = 4

Now,
Here, first term = 6,
common ratio = 4
then,
12^th term is = 6*4 ^{(12 - 1)}
= 6*4 ¹¹
= 6*4194304
=> 12^th term is = 25165824