The product of first four terms of a G.P. is 324 and the product of first three terms of the G.P. is

Question

The product of first four terms of a G.P. is 324 and the product of first three terms of the G.P. is 216 . Then the first term is\

Professor PC Thomas Classes · Answer

(e) : Let $\frac{a}{r}, a, a r, a r^{2}$ be the first four terms of the G.P., then $\left(\frac{a}{r}ight)(a)(a r)=216 \Rightarrow a^{3}=216 \Rightarrow a=6$\ Also, $\left(\frac{a}{r}ight)(a)(a r)\left(a r^{2}ight)=324$\ $\Rightarrow \quad(216)\left(6 r^{2}ight)=324 \Rightarrow r^{2}=\frac{1}{4} \Rightarrow r=\frac{1}{2}$\ $	herefore \quad$ First term $=\frac{a}{r}=\frac{6}{\frac{1}{2}}=12$\