Question

The prodect of first three numbers of a G.P. is 1000. if we add 6to its constant term and 7 to its 3rd term, the three terms form an A.P. find the terms of G.P.​

Answer 1

Answer:

AP. what are the terms of the GP?

Let the three numbers be a/r , a, ar.

a/r × a× ar = 1000

a^3 =1000

a = 10

According to the question ,

a/ r ,a+6, ar +7 form an ap

So, 2b = a+ c in an ap

2(a+6)=a/ r + ( ar + 7)

2(10+6)= 10/r + (10r+7)

2(16) = 10/r +10r+7

32–7= 10/r + 10r

25=10/r+ 10r

5= 2/r + 2 r

5r= 2+2r^2

2r^2–5r +2

On factorising the equation we get

r = 1/2 or r= 2

So ,if r= 1/2 ,

The gp is 20, 10,5

If r= 2,

The gp is 5,10,20.

Answer 2

Step-by-step explanation:

The GP is 5, 10, 20.........