Question
If for a G.P., $S_{4}=10 S_{4}$ find ' $r$ '.
✓
Answer
Here, $\mathrm{S}_{\mathrm{s}}=10 \mathrm{~S}_4$
$
\begin{array}{ll}
\therefore & \frac{a\left(r^2-1\right)}{(r-1)}=10\left[\frac{a\left(r^4-1\right)}{(r-1)}\right] \\
\therefore & r^3-1=10\left(r^4-1\right) \\
\therefore & \left(r^4-1\right)\left(r^4+1\right)=10\left(r^4-1\right) \\
\therefore & r^4+1-10 \\
\therefore & r^4=9 \\
\therefore & r^2-3 \\
\therefore & r= \pm \sqrt{3}
\end{array}
$
$
\begin{array}{ll}
\therefore & \frac{a\left(r^2-1\right)}{(r-1)}=10\left[\frac{a\left(r^4-1\right)}{(r-1)}\right] \\
\therefore & r^3-1=10\left(r^4-1\right) \\
\therefore & \left(r^4-1\right)\left(r^4+1\right)=10\left(r^4-1\right) \\
\therefore & r^4+1-10 \\
\therefore & r^4=9 \\
\therefore & r^2-3 \\
\therefore & r= \pm \sqrt{3}
\end{array}
$
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