Question

If sum of continuous three terms in an Arithmetic progression is 39/10 and product value of the same is 1 find 10

the such three terms in an Arithmetic mean.​

Answer 1

Answer:

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,