Question

Three numbers whose sum is 21 are in A.P. If 2,2,14 are added to them rwspectively, the resulting numbers are in G.P. Find the numbers in A.P.

Answer 1

let the numbers be a-d a and a+d , so they are in AP
so sum =3a =21 which implies a=7

so numbers are 7-d 7 and 7+d

7-d+2 7+2 7+d+14 they are in gp
so 9-d 9 21+d

so as rule of gp

9^2 = (9-d)* (21+d)
81 = (9-d) (21+d)
= 3 * 27
here i used a comparison method , otherwise you can use also quadratic equation solvung process also

so d= 6

so numbers in ap are

7-6 7 7+6
1 , 7 , 13 are the numbers......

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