Question

Fifth term of a G.P. is 2. Find the product of its 9 terms.

Answer 1

☯ GiveN :

Fifth term of the G.P is 2 (ar⁴ = 2).

$\rule{200}{1}$

☯ To FinD :

We have to find the product of its 9 terms of the G.P.

$\rule{200}{1}$

☯ SolutioN :

As, we have to find the find the product of first 9 terms of the G.P. So,

A.T.Q

Product of first 9 terms of G.P = a * ar * ar² * ar³ * ar⁴ *$\sf{ ar^5 * ar^6 * ar^7 * ar^8}$

Product of first 9 terms of G.P = $\sf{ a^9 r^36}$

We know that,

$\Large{\implies{\boxed{\boxed{\sf{ (a^n)^m = a^{nm} }}}}}$

Product of first 9 terms of G.P = $\sf{ (ar^{4})^9}$

Product of first 9 terms of G.P = $\sf{(2)^9}$

Product of first 9 terms of G.P = 512

$\Large{\implies{\boxed{\boxed{\sf{512}}}}}$

$\therefore$ Product of first 9 terms of G.P is 512.

Answer 2

Given,

Fifth term of a G.P. is 2.

→ ar⁴ = 2

To find :

The product of its 9 terms.

Solution ↓

Required product = $\sf{a \times ar \times ar^2 \times ar^3 \times \cdots \times ar^7 \times ar^8}$

$\sf{\implies Required\ product=a^9r^{1+2+3+4+5+6+7+8}}\\\\\sf{\implies Required\ product=a^9r^3^6}\\\\\sf{\implies Required\ product=(ar^4)^9}\\\\\sf{\implies Required\ product=2^9}\:\:\:\: \cdots \sf{(given)}\\\\\boxed{\boxed{\sf{\implies Required\ product=512}}}$