(C) Let the first term of the $G.P.$ be $a$ and the common ratio be $r$.Given that the third term $T_3 = ar^2 = 4$.We need to find the product of the

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(C) Let the first term of the $G.P.$ be $a$ and the common ratio be $r$.Given that the third term $T_3 = ar^2 = 4$.We need to find the product of the first $5$ terms:$P = a \times (ar) \times (ar^2) \times (ar^3) \times (ar^4)$$P = a^5 \times r^{(1+2+3+4)} = a^5 \times r^{10}$$P = (ar^2)^5$Substituting the value $ar^2 = 4$:$P = 4^5$.

Class 11 Mathematics Sequences and Series Geometric progression

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If the third term of a $G.P.$ is $4$,then the product of its first $5$ terms is:

IIT 1982 All IIT

A
$4^3$
B
$4^4$
C
$4^5$
D
None of these

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If the third term of a $G.P.$ is $4$,then the product of its first $5$ terms is:

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