Question

If the sum of $n$ terms of a G.P. is $3-\frac{3^{n+1}}{4^{2n}}$ then find the common ratio.

Answer 1

$S_n=3-\frac{3^{n+1}}{4^{2n}}$

$n=1$

$3-\frac{3^2}{4^2}=\frac{39}{16}$

$t_1=\frac{39}{16}$

$n=2$

$S_2=t_1+t_2=3-\frac{3^3}{4^4}=\frac{741}{256}$

$t_2=\frac{741}{256}-t_1=\frac{741}{256}-\frac{39}{16}$

$t_2=\frac{117}{256}$

$r=\frac{t_2}{t_1}$

$=\frac{117/256}{39/16}=\frac{3}{16}$

$r=3/16$.