# The sum of three numbers in A.P. is –3, and their product is 8. Find the numbers - Mathematics

Sum

The sum of three numbers in A.P. is –3, and their product is 8. Find the numbers

#### Solution

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

Sum = – 3

⇒ (a – d) + a (a + d) = – 3

⇒ 3a = – 3

⇒ a = – 1

Product = 8

⇒ (a – d) (a) (a + d) = 8

⇒ a (a^2 – d^2 ) = 8

⇒ (–1) (1 – d2 ) = 8

⇒ d2 = 9 ⇒ d = ± 3

If d = 3, the numbers are –4, –1, 2. If d = – 3, the numbers are 2, – 1, –4.

Thus, the numbers are –4, –1, 2, or 2, – 1, – 4.

Concept: Sum of First n Terms of an AP
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