Question

The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, find the AP.

Answer 1

Let the three terms in AP be 

a – d, a, a + d. 

So, a – d + a + a + d = 33 

or a = 11 

Also, (a – d) (a + d) = a + 29 

i.e., a² – d² = a + 29 

i.e., 121 – d² = 11 + 29 

i.e., d² = 81 

i.e., d = ± 9 

So there will be two APs and they are : 2, 11, 20, ... and 20, 11, 2, ...