Question

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.

Answer 1

Let the three terms in AP be a - d, a,a + d.

(i)

Given, Sum of three terms = 48.

⇒ a - d + a + a + d = 48

⇒ 3a = 48

⇒ a = 16.

(ii)

Given, Product of first & second terms exceeds 4 times the third term by 24.

⇒ (a - d) * a = 4(a + d) + 12

⇒ (16 - d) * 16 = 4(16 + d) + 12

⇒ 256 - 16d = 64 + 4d + 12

⇒ 256 - 76 = 20d

⇒ 180 = 20d

⇒ d = 9.

When a = 16 and d = 9:

⇒ a + d = 25

⇒ a = 16

⇒ a - d = 7.

Therefore, the AP is 7,16,25...

Hope this helps!