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Q.
$4^n$ term of the geometric progression $x, x^2+2, x^3+10$ is
Sequences and Series
Solution:
Given G.P. is $x , x ^2+2, x ^3+10$
$\therefore \left(x^2+2\right)^2=x\left(x^3+10\right) $
$\Rightarrow 4 x^2-10 x+4=0 $
$\Rightarrow 2 x^2-5 x+2=0 $
$\Rightarrow(2 x-1)(x-2)=0 $
$\therefore x=2,1 / 2 $
For $ x=2$
G.P. is $2, 6, 18, 54$
so next term of G.P. is $ 54$