Question

Find the three terms in AP whose sum is $36$ and product is $960$.

Answer 1

Let the three terms of an A.P. be (a + d) a (a - d) = 960
$\Rightarrow$(12 + d)(12 - d) = 80 $\Rightarrow$ 144 - $d^2$ 80 $\Rightarrow$ d = $\pm$ 8
Taking d - 8, we get the terms as 4, 12 and 20
Note : If d is taken as -8, then the same numbers are obtained, but in decreasing order.