three numbers are in A.P. and their sum is 15 , if 1, 4 and 19 are added to these numbers respectively the resulting numbers are in G.P.. find the numbers.

Let the given numbers in A.P. be ad,  a, a + d.

According to question,

Hence, the numbers are 5 – d, 5, 5 + d.

Adding 1, 4 and 19 in first, second and third number respectively, we get

Since these numbers are in G.P.

Hence the numbers are

26, 5, –16  or  2, 5, 8.

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