Question

the sum and product of three respective terms in AP is 15 and 80 find the terms of an arithmetic​

Answer 1

Call the numbers x-d, x, and x+d, d being the common difference between terms.

Then, x-d + x + x+d = 15 => 3x = 15, so x =5, and the other terms are 5-d and 5+d.

Now, (5-d)*5*(5+d) = 80 => (5-d)(5+d) = 25-d^2 = 16, so d^2 = 9 or d = + or - 3.

So, the three numbers are 2, 5, and 8. As a check, their sum and product are 15 and 80

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