Question

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

Answer 1

Sum of three numbers which are in A.P. = 3
Their product = -35
Let three numbers which are in A.P.
a – d, a, a + d
a – d + a + a + d = 3
⇒ 3a = 3,
⇒ a = `(3)/(3)` = 1
and
(a –  d) x a (a + d) = – 35
(1 – d) x 1 x (1 + d) = – 35
1² –  d² = – 35
1 –  d² = – 35
⇒ d² = 35 + 1 = 36
∴ d = ±6
If d = 6
∴ Number are 1 –  6, 1, 1 + 6
= – 5, 1, 7
If d = – 6
1 + 6, 1, 1 –  6
⇒ 7, 1, – 5
Hence numbers on A.P. are
– 5, 1, 7 or 7, 1, – 5.