Question -
Answer -
Consider a tobe the first term and r to be the common ratioof the G.P.
Then,
a1 = a, a2 = ar, a3 = ar2, a4 = ar3
From the question, wehave
a3 = a1 + 9
ar2 = a + 9 … (i)
a2 = a4 + 18
ar = ar3 + 18 … (ii)
So, from (1) and (2),we get
a(r2 – 1) = 9 … (iii)
ar (1– r2) = 18 … (iv)
Now, dividing (4) by(3), we get
-r = 2
r = -2
On substituting thevalue of r in (i), we get
4a = a +9
3a = 9
∴ a =3
Therefore, the firstfour numbers of the G.P. are 3, 3(– 2), 3(–2)2, and 3(–2)3
i.e., 3¸–6, 12, and–24.