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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...

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Natural Sum

The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/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.

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Series Sums

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

Prime AP

Stage: 4 Challenge Level: Challenge Level:1

First prove the common difference must be even and then that it must be divisible by 3. Think about possible remainders when the middle number is divided by 3. Consider two cases.