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

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

Step-by-step 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.