Question

If the product of five consecutive terms of a GP is $\frac{243}{32}$, then the middle term is

• A. $2/3$
• B. $3/2$
• C. $4/3$
• D. $3/4$
• E. $1$

Answer 1

The correct option is B $3/2$

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