State whether the statement is True/False.

Two numbers between 3 and 81 such that the series $3, G_{1}, G_{2}, 81$ forms a GP are 9 and 27.

True

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False

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Solution

The correct option is A True
Let $G_{1}$ and $G_{2}$ be two numbers between $3$ and $81$ such that the series $3, G_{1}, G_{2}, 81$ forms a GP.

Let $3$ be the first term and $r$ be the common ratio of the GP.

$a_{4} = 3 r^{3}$

$81 = 3 r^{3}$

$r^{3} = 27$

$r = 3$

For $r = 3$ ,

$G_{1} = a r = 3 (3) = 9$

$G_{2} = a r^{2} = 3 (3)^{2} = 27$

Thus, the required two numbers are 9 and 27.

Suggest Corrections

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