Question

Take any three consecutive even numbers and add them, say, 2 + 4 + 6 = 12, 4 + 6 + 8 = 18, 6 + 8 + 10 = 24, 8 + 10 + 12 = 30 and so on. Is there any pattern you can guess in these sums? What can you conjecture about them?

Answer 1

Answer:

The difference of the sum is 6 and the middle number is sum/3

Answer 2

Answer:

pattern  is that Sum is always multiple of 6

Another Pattern is that Sum is multiple of 3 of Middle term

Step-by-step explanation:

When any three consecutive even numbers are added then Sum will be a multiple of 6

Let say Three consecutive even numbers

are

2n ,  2n+ 2 ,  2n + 4

Sum = 2n + 2n+2 + 2n+4

= 6n + 6

= 6(n + 1)

pattern  is that Sum is always multiple of 6

6n + 6 = 3(2n + 2)

Another Pattern is that Sum is multiple of 3 of Middle term

Example

40  , 42 , 44

40 + 42 + 44

= 126

= 6 * 21

= 3 * 42