Insert two numbers between 3 and 81 so that t | vedclass

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Question

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 $G.P.$

Let $a$ be the first term a

Vedclass · Accepted Answer

$9,27$

Vedclass · Answer

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 $G.P.$

Let $a$ be the first term and $r$ be the common ratio of the $G.P.$

$	herefore 81=(3)(r)^{3}$

$\Rightarrow r^{3}=27$

$	herefore r=3$ (Talking real roots only)

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 $27$

Insert two numbers between $3$ and $81$ so that the resulting sequence is $G.P.$

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