the sum of first three terms of a G.P is 49:15 and their produsct is 1 then find the commen ratio and the terms of g.p
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Answer:
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Step-by-step explanation:
Let
r
a
,a,ar be the first terms of the G.P.
r
a
+a+ar=
10
39
....(1)
(
r
a
)(a)(ar)=1...(2)
From (2) we obtain a
3
=1⇒a=1 (considering real roots only)
Substituting a=1 in equation (1), we obtain
r
1
+1+r=
10
39
⇒1+r+r
2
=
10
39
r
⇒10+10r+10r
2
−39r=0
⇒10r
2
−29r+10=0
⇒10r
2
−25r−4r+10=0
⇒5r(2r−5)−2(2r−5)=0
⇒(5r−2)(2r−5)=0
⇒r=
5
2
or
2
5
corresponding terms of the G.P
1. when r=
5
2
⇒
2
5
,1,
5
2
2. when r=
2
5
⇒
5
2
,1,
2
5
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