Question

three numbers are in AP and their sum is 21 .If 1,5,15 are added to them respectively,they form GP. The numbers are
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Answer 1

Answer:

5, 7, 9

Step-by-step explanation:

Let the numbers be x, y and z.

x+ y + z= 21.

In an AP, the middle term of an odd series is its AVERAGE.

Thus, the middle number y= 21/3= 7

We get: x+ z= 21-7= 14. { Eqn. #1

In a GP, the middle term of an odd series is its SQUARE ROOT.

Thus, √[(x+1) x (z+15)]= 7+5= 12

(x+1) x (z+15)= 144. {Eqn. #2

Solving the two equations, we get the answer.