Question

The sum of three numbers in AP is 3 and their product is –35. Find the numbers.

Answer 1

Let the required numbers be (a – d), a and (a + d).

Then (a – d) + a + (a + d) = 3

⇒ 3a = 3 

⇒ a = 1

Also, (a – d) . a . (a + d) = –35

⇒ a(a² – d²) = –35

⇒ 1.(1 – d²) = –35

⇒ d² = 36

⇒ d = ±6

Thus, a = 1 and d = ±6

Hence, the required numbers are (–5, 1 and 7) or (7, 1 and –5).