Q. 135.0( 6 Votes )

# The sum of three consecutive terms in an A.P. is 6 and their product is –120. Find the three numbers.

We know that the three consecutive terms of an A.P. may be taken as a – d, a, a + d.

Given, a – d + a + a + d = 6

3a = 6

a = 6/3 = 2

Also given (a – d) (a) (a + d) = -120

We know that (a – b) (a + b) = a2 – b2

(a2 – d2) (2) = -120

(22 – d2) = -120/2

4 – d2 = -60

d2 = 60 + 4 = 64

d = 8

So, the numbers are

a – d = 2 – 8 = -6

a = 2

a + d = 2 + 8 = 10

The three consecutive numbers are -6, 2, 10.

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