Question

in a geometrical progression the product of the first three terms is 27 by 8 then its middle term will be

Answer 1

let the g.p be

a/r , a , ar

where r is common ratio

thus product = 27/8

(a/r)*a*(ar) = 27/8

a³ = (3/2)³

a = 3/2

thus middle term = 3/2

Answer 2

Given : The product of first three terms of a GP is 27/8

To find : It's middle term

Solution :

We know that a geometric progression is a sequence of numbers in which common ratio between two consecutive terms is always same.

Let's assume that the first three terms of GP be a/r, a and ar where a is first term and r is common ratio.

Now, according to the question :-

=> a/r × a × ar = 27/8

=> a × a × a = 27/8

=> a³ = (3/2)³

=> a = (3/2)

Therefore the middle term of the GP = a = (3/2).

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