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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)

Vedclass · Accepted Answer

$16$

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 $ar^4 = 32$.Substituting $a = 2$ in the equation $ar^4 = 32$,we get $2r^4 = 32$,which implies $r^4 = 16$.Since $16 = 2^4$,we have $r = 2$.The third geometric mean is the fourth term of the sequence,which is $g_3 = ar^3$.Substituting the values,$g_3 = 2 	imes (2)^3 = 2 	imes 8 = 16$.

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

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