Answer:
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.