Question

If $S_3=125,S_6=152$, find $r$.

Answer 1

$S_3=125,S_6=152$

$S=\frac{a(r^n-1)}{r-1}$

$S_3=\frac{a(r^3-1)}{2}=125⟹a(r^3-1)=250$

$S_6=\frac{a(r^6-1)}{5}=152⟹a(r^6-1)=760$

$a(r^6-1)=760$

$a(r^3-1)(r^3+1)=760$

$(r^3+1)=\frac{760}{250}$

$r^3=\frac{76}{25}-1$

$r=1.268$