Question

The fourth element is square the 2nd term & 3rd element is 27. Find GP​

Answer 1

Step-by-step explanation:

Let the first term be a and common ratio be x. So 2nd term is ax and third term is

$a {x}^{2}$

Fourth term is

$a{x}^{3}$

So it is given that Fourth term is square of second term

${(ax)}^{2} = a {x}^{3} = > {a}^{2} {x}^{2} = a {x}^{3} = >$

${a}^{2} {x}^{2} - a {x}^{3} = > a {x}^2(a - x) = 0 = >$

Since a and x are non zero quantities So a=x. It is also given that third term is 27 so

$a {x}^{2} = 27 = > {x}^{3} = 27 = > x = 3$

So the G.P. is 3,9,27,81,243,729,2187,6561,... Hope it helps you.