Question

the sum of first term 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 a - d, a, a + d be three terms of an AP.
Given that sum of the three terms is 33.
That is, a - d + a + a + d = 33
3a = 33
a = 33/3 =11
Product of the first term and third term exceeds the second term by 29.
(a - d)(a + d) = a + 29
When a = 11, d = 9, AP: 2, 11, 20
When a = 11, d = -9, AP:20, 11, 2