Hi Math Central,
The following problem was given to our 8th gr. class........
How many positive multiples of 10 that are less than 1000 are the sum of four consecutive integers?
Thanks for helping......
Note that 10 = 1+2+3+4; now adding 5 to each of those we find
now adding 5 to each of those we find
and so on, thus there's a solution for 10, 30, 50, ... .
On the other hand it is easy to check that 20 is not the sum of 4 consecutive numbers; now if 40 is the sum of 4 consecutive numbers we could subtract 5 off each of these numbers and find a solution for 20 which we already know is not possible; continuing in this manner we find no solution for 20, 40, 60, ... .