Question

If there are $4$ G.M.s between $2$ and $486,$ then find the $4th$ G.M. is

• A. $6$
• B. $18$
• C. $54$
• D. $162$

Answer 1

The correct option is C $54$

Common ratio of the series is $r={\left(\frac{b}{a}\right)}^{\frac{1}{n+1}}$
$\Rightarrow {\left(\frac{486}{2}\right)}^{\frac{1}{4+1}}$
$\Rightarrow (243{)}^{\frac{1}{5}}=3$
Hence four G.M. are $6,18,54,162$
Then fourth G.M $=54$
'