Arithmetic sequences

problem

Unravelling Sequences

Age

7 to 11

Challenge level

Can you describe what is happening as this program runs? Can you unpick the steps in the process?
problem

Cherries Come in Twos

Age

7 to 11

Challenge level

Susie took cherries out of a bowl by following a certain pattern. How many cherries had there been in the bowl to start with if she was left with 14 single ones?
problem

Investigating Pascal's Triangle

Age

7 to 11

Challenge level

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

Many Matildas

Age

11 to 14

Challenge level

MatildaMatildaMatil... What is the 1000th letter?
problem

Maxagon

Age

11 to 14

Challenge level

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

Natural Sum

Age

14 to 16

Challenge level

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.
problem

Prime Sequences

Age

16 to 18

Challenge level

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

Speedy Summations

Age

16 to 18

Challenge level

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

Polite Numbers

Age

16 to 18

Challenge level

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?
interactivity
Proof Sorter - Sum of an Arithmetic Sequence

Age

16 to 18

Challenge level

Put the steps of this proof in order to find the formula for the sum of an arithmetic sequence