If the produce of five consecutive terms of a G.P. is (243/32) , then the middle term is

Question

If the produce of five consecutive terms of a G.P. is (243/32) , then the middle term is (A) (2/3) (B) (3/2) (C) (4/3) (D) (3/4)

Tardigrade Admin · Accepted Answer

Let five consecutive terms of GP are (a/r2), (a/r), a, a r, a r2. According to the question, (a/r2) × (a/r) × a × a r × a r2=(243/32) ⇒ a5=((3/2))5 ∴ a=(3/2), which is the middle term.

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

$\frac{2}{3}$

$\frac{3}{2}$

$\frac{4}{3}$

$\frac{3}{4}$

1

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

Q. If the produce of five consecutive terms of a G.P. is 32243​ , then the middle term is

32​

23​

34​

43​

1