Question

Plz help, I don't understand this.

Answer 1

see explanation

Explanation:

consecutive even integers have a difference of 2 between them

for example 2, 4, 6 are 3 consecutive even integers

In general if we let the first integer be k then the next 2 integers are

k + 2 and k + 4

the sum of these equals 4 times the first integer, that is 4k, hence

k + k + 2 + k + 4 = 4k

3k + 6 = 4k ( subtract 3k from both sides )

6 = k

the 3 consecutive integers are

k = 6

k + 2 = 6 + 2 = 8

k + 4 = 6 + 4 = 10

that is 6, 8 and 10

note that sum = 6 + 8 + 10 = 24

and 4 × 6 = 24

confirming the sum of the 3 integers equals 4 times the first integer