let a 6 b 24 be a GP find a and bSolutiona 6 b 24 are terms

let a, 6, b, 24 be a G.P find a and b

a, 6, b, 24 are terms of a G.P

Let r be the common difference such that:

6= a*r .........(1)

b= 6*r ..........(2)

24= b*r .........(3)

Let us use the substitution methos:

substitue (2) in (3):

==> 24 = b*r = (6r)*6 = 6r^2

==> 24= 6r^2

Now divide by 6:

==> r^2 = 24/6 = 4

==> r= 2

Now substitue in (2):

b= 6*r = 6*2 = 12

==> b= 12

Now let ussubstitue in (1):

6= a*r

==> a= 6/2 = 6/2 = 3

==> a= 3

==> 3, 6, 12, 24 are terms of a G.P with r= 2