SOLUTION: Show that the sum of any three consecutive numbers is a multiple of 3. Show that the sum of any four consecutive numbers is always even.

Algebra.Com
Question 878328: Show that the sum of any three consecutive numbers is a multiple of 3.
Show that the sum of any four consecutive numbers is always even.

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Show that the sum of any three consecutive numbers is a multiple of 3.
n-1 + n + n+1 = 3n
----------------------
Show that the sum of any four consecutive numbers is always even.
2n + 2n+1 + 2n+2 + 2n+3 = 8n + 6

RELATED QUESTIONS

show that the sum of any consecutive odd whole numbers has any factor of 5. (answered by solver91311)
Show that the sum of any 5 consecutive counting numbers must have a factor of... (answered by khwang)
Show that 1 greater than the sum of the squares of any three consecutive integers is... (answered by richard1234)
The sum of three consecutive numbers is 27.What are the three numbers?Show your work (answered by jim_thompson5910,Alan3354)
Show that the sum of two consecutive numbers is not even. (answered by josgarithmetic)
find four consecutive numbers such that the sum of the first three numbers is twelve more (answered by Maths68)
prove that the product of any three consecutive numbers is even. So far I have tried , (answered by josgarithmetic,tenkun,amalm06,ikleyn)
1. Show that the sum of any two odd numbers is always an even number. 2. Show that the... (answered by ewatrrr)
the sum of the squares of 3 consecutive numbers is 50. Let x be the smallest of the... (answered by Timnewman)