Arithmetic sequences

In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.

MatildaMatildaMatil... What is the 1000th letter?

What's the greatest number of sides a polygon on a dotty grid could have?

The picture illustrates the sum 1 + 2 + 3 + 4 = (4 × 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.

Find the sum, f(n), of the first n terms of the sequence: 0, 1, 1, 2, 2, 3, 3........p, p, p +1, p + 1,..... Prove that f(a + b) - f(a - b) = ab.

This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?

Watch the video to see how to add together an arithmetic sequence of numbers efficiently.

Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.

A polite number can be written as the sum of two or more consecutive positive integers, for example 8+9+10=27 is a polite number. Can you find some more polite, and impolite, numbers?