Question

Find three terms in A.P. whose sum is 129 and whose product is 79335.

Answer 1

Answer:

Let the three numbers be a−d,a,a+d.

It is given that the sum of the numbers is 36, therefore,

a−d+a+a+d=36

⇒3a=36

⇒a= 336

=12......(1)

It is also given that the product of the numbers is 1620, therefore using equation 1 we have,

(a−d)(a)(a+d)=1620

⇒(12−d)(12)(12+d)=1620

⇒(12−d)(12+d)=

12

1620

⇒12 2 −d 2=135

⇒d 2=144−135

⇒d 2=9

⇒d=−3,d=3

With a=12 and d=3, the three numbers are as follows:

a−d=12−3=9

a−d=12−3=9a=12

a−d=12−3=9a=12a+d=12+3=15

Thus, the numbers are 9,12 and 15.

With a=12 and d=−3, the three numbers are:

a−d=12−(−3)=12+3=15

a−d=12−(−3)=12+3=15a=12

a−d=12−(−3)=12+3=15a=12a+d=12−3=9

Thus, the numbers are 15,12 and 9.