Question

the sum of three numbers in AP is 15.if first two term are decreased by 1 .and last term is increased by 1. then the reasulting term is in GP, find the numbers.​

Answer 1

Answer is attached.......

Hope it help

Answer 2

Answer:

Let the three numbers be a-d, a and a+d

Given that a-d+a+a+d = 15

Hence a = 5

5-d - 1 and 5-1

= 4-d and 4

Last term is increased by 1

So 5+d+1 = 6+d

Resulting terms are in GP

4-d, 4 and 6+d are in GP

Thus 4*4 = (4-d)(6+d)

16 =24+4d-6d-d*d

0 = 8-2d -d*d

d square +2d -8= 0

dsquare +4d -2d -8= 0

d(d+4) -2(d+4) = 0

Thus d can be either -4 or 2

Now if d = 2

Numbers are 3 , 5 and 7

If d = -4,

Numbers are 1, 5 and 9

Hope it helps you.

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