Question

Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers

Answer 1

Given: 

Sum of first three terms is 27

Let us assume the first three terms as a – d, a, a + d [where a is the first term and d is the common difference]

So, sum of first three terms is

a – d + a + a + d = 27

3a = 27

a = 9

It is given that the product of three terms is 648

So, a³ – ad² = 648

Substituting the value of a = 9, we get

9³ – 9d² = 648

729 – 9d² = 648

81 = 9d²

d = 3 or d = – 3

Hence, the given terms are a – d, a, a + d which is 6, 9, 12.