Question

Find the three natural numbersin AP whose sum is 36 and the product is 1620

Answer 1

Let the three numbers in A.P be (a-d), a and (a+d)

Sum of three numbers is 36

a-d + a + a+d = 36

3a = 36

a = 12

Product of three numbers is 1620

(a-d) × a × (a+d) = 1620

a (a²- d²) = 1620

12.(144 -nd²) = 1620

144 - d² = 1620 / 12

144 - 135 = d²

d² = 9d = 3

Therefore three numbers in A.P are (12-3),12,(12+3)

⇒9 , 12 , 15.

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