Question

If second term of a G.P. is 2 and the sum of its infinite terms is 8, then its first term is
(a) 1/4
(b) 1/2
(c) 2
(d) 4

Answer 1

(d) 4

$$\begin{gathered} a_2=2 \\ \therefore ar=2........\left(\mathrm{i}\right) \\ \mathrm{Also},S_{\infty }=8 \\ \Rightarrow \frac{a}{\left(1-r\right)}=8 \\ \Rightarrow \frac{a}{\left(1-{\displaystyle \frac{2}{a}}\right)}=8\left[\mathrm{Using}\left(\mathrm{i}\right)\right] \\ \Rightarrow a^2=8\left(a-2\right) \\ \Rightarrow a^2-8a+16=0 \\ \Rightarrow {\left(a-4\right)}^2=0 \\ \Rightarrow a=4 \end{gathered}$$