Test Index

Sequence and Series

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Question : 64 of 86

Marks: +1, -0

In a GP series, the product of the first three terms

\frac{27}{8}

, the middle term is

$\frac{3}{2}$
$\frac{2}{3}$
$\frac{2}{5}$
None of these

Solution:

Concept:

In a geometric progression (GP), the product of three consecutive terms equals the cube of the middle term.

Explanation:

Let the three terms be

\frac{a}{r}

,

a

,

ar

. Their product is

\frac{a}{r} \cdot a \cdot ar = a^{3}

.

Given

a^{3} = \frac{27}{8}

.

Taking cube root,

a = \frac{3}{2}

.

The middle term is

a = \frac{3}{2}

.

Answer:

\frac{3}{2}

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