The second term of an infinite geometric series is \(-1 / 2\) and the third term is \(1 / 4\). Find the sum of the series ____________
Explanation
\begin{aligned}
T_{2} &=a r=-\frac{1}{2} \ldots \ldots \ldots \ldots . .(1) \\
T_{3}=& a r^{2}=\frac{1}{4} \ldots \ldots \ldots \ldots \ldots(2) \\
& \text { eqn }(2) \text { divided by eqn }(1) \text { gives } \\
\frac{a r^{2}}{a r} &=\frac{1}{-1} .
\end{aligned}
\text { from which } \begin{aligned}
r &=\frac{1}{4} \times-2 \\
r &=-\frac{1}{2} \\
a r &=-\frac{1}{2} ; a=\frac{-1}{1}=1 \\
s, &=\frac{a}{1-r}=\frac{1}{1+\frac{1}{2}}=\frac{1}{2} \\
s, &=\frac{3}{2}
\end{aligned}