# The sum of first three terms of an AP is 48. If the product of first and second terms exceeds 4 times the third term by 12. Find the AP.

Let the numbers be (a - d), a, (a + d).

Now, sum of the numbers = 48

(a - d) + a + (a + d) = 48

3a = 48

a = 16

Now, we are given that,

Product of first and second terms exceeds 4 times the third term by 12.

(a - d) × a = 4(a + d) + 12

a2 - ad = 4a + 4d + 12

On putting the value of a in the above equation, we get,

256 - 16d = 64 + 4d + 12

20 d = 180

d = 9

The numbers are a - d, a, a + d

i.e. the numbers are 7, 16, 25.

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