Question

the product of first three terms of a GP is 1000 if we add 6 to its second term and 7 to its third term resulting three terms form an ap find the terms of the GP​

Answer 1

Product of first three terms of GP = 1000 (Given)

Number added to the second term = 6 (Given)

Number added to the third term = 7 (Given)

Let the three numbers be = a, ar and a/r

Thus,

a × ar × a/r = 1000

a³ =1000

a = 10

Now,

a/ r, a+6, ar +7 will form an AP

Thus, 2b = a+ c are in AP

Substituting the value -

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

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

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

= 25 = 10/r + 10r

5 = 2/r + 2r

5r = 2+2r²

Factorizing the equation -

r = 1/2 or r = 2

Thus, if r = 1/2, then GP is 20, 10,5

If r = 2,  then GP is 5,10,20.