Pthen,2ence, the numbers are 21,4. Find four numbers forming a GP. in

1.	Pthen,2ence, the numbers are 21,4. Find four numbers forming a GP. in which the third term is gterm by 9 and the second term is greater than 4 term by 18.L. Let the four terms of G.P. be a, ar,ar2,arven:
Answer» Let the first term be a and the ratio r. The four terms then are a,ar,ar^2 and ar^3 given , ar^2 = a + 9 ….(1) and ar=ar^3+18 …. (2) from (1), a*(r^2–1)=9…(3) from (2), ar(r^2–1)=-18..(14) (3)/(4) gives r=-2 substituting this in (1) 4a=a+9=>a=3. So the terms are 3,-6,12,-24 Like my answer if you find it useful!

Pthen,2ence, the numbers are 21,4. Find four numbers forming a GP. in which the third term is gterm by 9 and the second term is greater than 4 term by 18.L. Let the four terms of G.P. be a, ar,ar2,arven:

Answer»

Let the first term be a and the ratio r.

The four terms then are a,ar,ar^2 and ar^3

given , ar^2 = a + 9 ….(1) and

ar=ar^3+18 …. (2)

from (1), a*(r^2–1)=9…(3)

from (2), ar(r^2–1)=-18..(14)

(3)/(4) gives r=-2

substituting this in (1) 4a=a+9=>a=3.

So the terms are 3,-6,12,-24

Like my answer if you find it useful!