The first term of a geometric series is 1. The sum of its third and fifth terms is 90. Find the ratio of the geometric series
The first term of a geometric series is 1. The sum of its third and fifth terms is 90. Find the ratio of the geometric series
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Step-by-step explanation:
Let r be the common ratio of the G.P. It is given that the first term a=1.
Now, a
3
+a
5
=90
⇒ar
2
+ar
4
=90
⇒r
2
+r
4
=90
⇒r
4
+r
2
−90=0
⇒r
4
+10r
2
−9r
2
−90=0
⇒(r
2
+10)(r
2
−9)=0
⇒r
2
−9=0
⇒r=±3
Hence, the common ratio of the given G.P. is 3 or −3.
Step-by-step explanation:
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