Question

Four Geometric means are inserted between 2 and 486. Find the common ratio of the resulting G.P.

• A. 3
• B. 4
• C. 2
• D. 5

Answer 1

The correct option is A

3

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.

$t_n$ = $a.r^{n-1}$

$\Rightarrow$ 2 $\times$ ${\left(r\right)}^{6-1}$ = 486

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

$\Rightarrow r=3$