Question

Show that the sum of any four consecutive odd numbers is divisible by 8

Answer 1

Answer:

If "x is the smallest of four consecutive odd numbers," then they are:

x, (x+2), (x+4) and (x+6)

Their sum is:

x + (x+2) + (x+4) + (x+6) = 4x + 12 = 4(x+3) [factor out 4]

Note: To meet the criteria, "the sum of four consecutive odd numbers is divisible by 8," then (x+3) must be even. That means that x must be an odd integer.

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Answer 2

Step-by-step explanation:

Let the consecutive odd numbers be $2n-3$ , $2n-1$ , $2n+1$ , $2n+3$

sum, $S=(2n-3)+(2n-1)+(2n+1)+(2n+3)=8n$      , which is divisible by 8

Hence sum of any 4 consecutive odd numbers is divisible by 8