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.