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Question

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

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Solution

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).

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