If three geometric means be inserted between 2 and 32 , then third geometric mean will be

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Gujarati

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8. Sequences and Series

easy

If three geometric means be inserted between $2$ and $32$, then the third geometric mean will be

$8$

$4$

$16$

$12$

$a = 2,\;ar = {g_1},\;a{r^2} = {g_2},\;a{r^3} = {g_3}$ and $a{r^4} = 32$

Now $2 \times {r^4} = 32$

$\Rightarrow {r^4} = 16 = {(2)^4} $

$\Rightarrow r = 2$.

Then third geometric mean $ = a{r^3} = 2 \times {2^3} = 16$.

Aliter : By formula, ${G_3} = 2.{\left( {\frac{{32}}{2}} \right)^{3/4}} = 2\;.\;8 = 16$.

Standard 11

Mathematics

medium

hard

(IIT-1966)

easy

(AIEEE-2002)

normal

(KVPY-2020)

hard