Single Choice

The third term of a Geometric Progression is $$4$$. The product of the first five terms is :

A$$4^3$$
B$$4^5$$
Correct Answer
C$$4^4$$
Dnone of these

Solution

Let $$a$$ be the first term of a G.P. and $$r$$ be the common ratio.
$$\therefore$$ First five terms of a G.P. are $$a, ar, $$ $$ar^2, ar^3, ar^4$$
$$\therefore $$ Third terms $$= ar^2 = 4$$
Product of first five terms $$=$$ $$(a^5)(r^{1+2+3+4})=(a^5)(r^{10})$$
$$\Rightarrow (ar^2)^5=4^5$$

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