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(C) Let the three geometric means be $g_1, g_2, g_3$ between $2$ and $32$.Then the sequence $2, g_1, g_2, g_3, 32$ forms a Geometric Progression $(GP)

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$16$

Vedclass · Answer

(C) Let the three geometric means be $g_1, g_2, g_3$ between $2$ and $32$.Then the sequence $2, g_1, g_2, g_3, 32$ forms a Geometric Progression $(GP)$.Here,the first term $a = 2$ and the fifth term $ar^4 = 32$.$2 	imes r^4 = 32 \Rightarrow r^4 = 16$.Since $r^4 = 2^4$,we have $r = 2$ (taking the positive common ratio).The third geometric mean is $g_3 = ar^3$.$g_3 = 2 	imes (2)^3 = 2 	imes 8 = 16$.

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

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