### Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

### Prime AP

Show that if three prime numbers, all greater than 3, form an arithmetic progression then the common difference is divisible by 6. What if one of the terms is 3?

### Series Sums

Let S1 = 1 , S2 = 2 + 3, S3 = 4 + 5 + 6 ,........ Calculate S17.

# Natural Sum

##### Stage: 4 Challenge Level:

The picture illustrates the sum $1 + 2 + 3 + 4 = (4 \times5)/2$. Prove the general formula for the sum of the first $n$ natural numbers and the formula for the sum of the cubes of the first n natural numbers. See the problem Picture Story .