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

Answer:

Given,

Sum of first three terms is 27

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

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,

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.