Question

Three numbers a,b,c are in G.P. if a,b, c-64 are in A.P and a,b-8, c-64 are in G.P,then the sum of numbers may be

Answer 1

Answer:

is given that the product of the terms is 216, therefore,

r

a

×a×ar=216

⇒a

3

=216

⇒a

3

=6

3

⇒a=6.....(1)

It is also given that the sum of the terms is 21, therefore using equation 1 we have,

r

a

+a+ar=21

⇒

r

6

+6+6r=21

⇒

r

6

+6r=21−6

⇒6(

r

1

+r)=15

⇒

r

1+r

2

=

6

15

=

2

5

⇒2r

2

+2=5r

⇒2r

2

−5r+2=0

⇒2r

2

−4r−r+2=0

⇒2r(r−2)−1(r−2)=0

⇒(2r−1)(r−2)=0

⇒(2r−1)=0,(r−2)=0

⇒r=

2

1

,r=2

With a=6 and r=

2

1

, the three terms of G.P are as follows:

r

a

=

2

1

6

=6×2=12

a=6

ar=6×

2

1

=3

Thus, the terms are 12,6 and 3.

With a=6 and r=2, the three terms are:

r

a

=

2

6

=3

a=6

ar=6×2=12

Thus, the terms are 3,6 and 12.