Question

find three consecutive negative integers such that six times the largest is equal to the twice sum of the two smaller integers.

Answer 1

The consecutive negative integers are -3, -4 and -5.

Explanation:

Let the three consecutive negative integers be k, (k-1) and (k -2)

Now, according to the question:

6(Largest Integer) = 2( Sum of smaller two Integers)

or, 6 (k) = 2( (k-1) + (k-2))

⇒ 6k = 2(2k -3)

or, 6k = 4k - 6

or, 6k - 4k = -6

or, 2k = -6 ⇒ k = -3

Hence, the largest negative integer = -3

The next two consecutive negative integer are (k-1) and (k-2) = (-3-1) and (-3-2)

= -4 and -5

Hence, the consecutive negative integers are -3, -4 and -5.