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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

Show that if three prime numbers, all greater than 3, form an arithmetic progression then the common difference of the progression is divisible by 6. Find some examples of three primes which include the number 3 and form an AP, and show that in every such case the common difference is not divisible by 6.