Question

The product of three terms of a GP is 512. If 8 is added to the first term and 6 othe second term, find the new terms form an AP​

Answer 1

Step-by-step explanation:

8/r + 8, 14, 8r are in AP. When r = ½, the numbers are 16, 8, 4. When r = 2, the numbers are 4, 8, 16. Hence option (2) is the answer.

Answer 2

Step-by-step explanation:

Let a/r, a, ar be the terms in GP.

Then product = (a/r)a(ar) = 512

a3 = 512

So a = 8

(a/r)+8 , a+6, ar are in AP.

8/r + 8, 14, 8r are in AP.

So 28 = 8/r + 8 + 8r

20 = 8/r + 8r

20r = 8+8r2

8r2-20r+8 = 0

2r2-5r+2 = 0

(2r-1)(r-2) = 0

r = ½ or r = 2

When r = ½, the numbers are 16, 8, 4.

When r = 2, the numbers are 4, 8, 16.