Question

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

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Answer 1

The resultant G.P. will have 6 terms including 2 and 486.

The first term of the G.P. is 2 and the 6^{th} 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 $\times$ ${\left(r\right)}^{6-1}$ = 486

$r^5$ = 243 = $3^5$

$\Rightarrow r=3$