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 a – d, a, a + d are the three terms in AP

So,

Sum = a – d + a + a + d = 48

3a = 48

Or a = 16

And,

a(a – d) = 4 (a + d) + 12

16 (16 – d) = 4(16 + d) + 12

256 – 16d = 64 + 4d + 12 = 4d + 76

256 – 76 = 4d + 16d

180 = 20d

d = 9

Which implies:

Numbers are : (7, 16, 25)