Fiod fewer number forming a goomathic para
en in Lohich the trend term is greater than the
+ by q, and the becend team is greater than the
th
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Answer:
Let a be the first term and r be the common ratio of the G.P
a
1
=a, a
2
=ar, a
3
=ar
2
, a
4
=ar
3
By the given condition,
a
3
=a
1
+9
⇒ar
2
=a+9....(1)
a
2
=a
4
+18
⇒ar=ar
3
+18....(2)
From (1) and (2), we get
a(r
2
−1)=9....(3)
ar(1−r
2
)=18....(4)
Dividing (4) and (3), we get
a(r
2
−1)
ar(1−r
2
)
=
9
18
⇒−r=2
⇒r=−2
Substituting the value of r in (1), we get
4a=a+9
⇒3a=9
∴a=3
⇒a
1
=3
⇒a
2
=3(−2)=−6
⇒a
3
=3(−2)
2
=12
⇒a
4
=3(−2)
3
=−24
Thus the first four numbers of the G.P are 3,-6,12 and -24.
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