4 G.Ms are inserted between 2 and 486, then the common ratio of the resulting G.P is___

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Solution

The resultant G.P. will have 6 terms including 2 and 486.
The first term of the G.P. is 2 and the $6^{t h}$ term is 486.
$\Rightarrow 2, G_{1}, G_{2}, G_{3}, G_{4},$ 486 are in G.P.
$t_{1} = 2 t_{6} = 486$
Let the common ratio of be r.
$\Rightarrow 2 \times (r)^{6 - 1} = 486 r^{5} = 243 = 3^{5} \Rightarrow r = 3$

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