Question

three numbers are in ap and thier sum is 21. if 1, 5, 15 are added to then respectively they form a gp ​

Answer 1

Answer:5,7,9 or23,-9,7

Step-by-step explanation:

The terms in AP are a-d, a, a+d

So their sum 3a=21, a=7

So the terms are 7-d, 7, 7+d

By adding 1, 5, 15 respectively

8-d, 12, 22+d

12^2=(8-d)(22+d)

144= 176-14d-d^2

d^2+14d-32=0

By factoring, we get

d^2-2d+16d-32=0

d(d-2)+16(d-2)=0

(d+16)(d-2)=0

d=-16, d=2

So the numbers are

5, 7, 9

23, 7, -9