Question

If the produce of five consecutive terms of a $G.P.$ is $\frac{243}{32}$ , then the middle term is

• A. $\frac{2}{3}$
• B. $\frac{3}{2}$
• C. $\frac{4}{3}$
• D. $\frac{3}{4}$
• E. 1

Answer 1

Answer: (B)

Let five consecutive terms of GP are $\frac{a}{r^{2}}, \frac{a}{r}, a, a r, a r^{2}$.
According to the question,
$\frac{a}{r^{2}} \times \frac{a}{r} \times a \times a r \times a r^{2}=\frac{243}{32} \Rightarrow a^{5}=\left(\frac{3}{2}\right)^{5}$
$\therefore a=\frac{3}{2}$, which is the middle term.