Question

If the product of 3 consecutive terms of G.P is 27 find the middle term.

Answer 1

(a/g)*a*(ag)=27
a^3=27
a=3
middle term is 3

Answer 2

Given,

Product of  3 consecutive terms of GP = 27

To find,

Middle term of GP

Solution,

The consecutive numbers in GP have a common ratio.

General form of GP is :$a, ar, ar^{2} , ar^{3} , ar^{4}, .. ar^{n}$

Here a is the first term

and r is the common ratio.

So, let the 3 consecutive numbers of GP be $a, ar, ar^{2}$.

Given product of these 3 numbers = 27

⇒$a*ar*ar^{2} = 27$

⇒$a^{3} r^{3} = 27$

⇒$(ar)^{3} = 27$

⇒$(ar)^{3} = 3^{3}$

⇒$ar=3$

So we considered $a, ar, ar^{2}$ as the GP , therefore middle term is ar.

Hence,the middle term of GP is 3.