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Broad Topics > Sequences, Functions and Graphs > Arithmetic sequence

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Shifting Times Tables

Stage: 3 Challenge Level: Challenge Level:1

Can you find a way to identify times tables after they have been shifted up?

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Multiplication Square Jigsaw

Stage: 2 Challenge Level: Challenge Level:1

Can you complete this jigsaw of the multiplication square?

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100 Square Jigsaw

Stage: 1 Challenge Level: Challenge Level:1

Can you complete this jigsaw of the 100 square?

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Squares in Rectangles

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

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Coordinate Patterns

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

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More Number Pyramids

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

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Proof Sorter - Sum of an AP

Stage: 5 Challenge Level: Challenge Level:1

Use this interactivity to sort out the steps of the proof of the formula for the sum of an arithmetic series. The 'thermometer' will tell you how you are doing

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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 is divisible by 6. What if one of the terms is 3?

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Days and Dates

Stage: 4 Challenge Level: Challenge Level:1

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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Domino Sequences

Stage: 1 Challenge Level: Challenge Level:1

Find the next two dominoes in these sequences.

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Domino Number Patterns

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Can you work out the domino pieces which would go in the middle in each case to complete the pattern of these eight sets of 3 dominoes?

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Buzzy Bee

Stage: 1 Challenge Level: Challenge Level:1

Buzzy Bee was building a honeycomb. She decided to decorate the honeycomb with a pattern using numbers. Can you discover Buzzy's pattern and fill in the empty cells for her?

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Next Domino

Stage: 1 Challenge Level: Challenge Level:1

Which comes next in each pattern of dominoes?

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Odds, Evens and More Evens

Stage: 3 Challenge Level: Challenge Level:1

Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

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Charlie's Delightful Machine

Stage: 3 and 4 Challenge Level: Challenge Level:1

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

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A Little Light Thinking

Stage: 4 Challenge Level: Challenge Level:1

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

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Slick Summing

Stage: 4 Challenge Level: Challenge Level:1

Watch the video to see how Charlie works out the sum. Can you adapt his method?

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Speedy Summations

Stage: 5 Challenge Level: Challenge Level:1

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

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Cellular

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

Cellular is an animation that helps you make geometric sequences composed of square cells.

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Prime Sequences

Stage: 5 Challenge Level: Challenge Level:1

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

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Mobile Numbers

Stage: 1 and 2 Challenge Level: Challenge Level:1

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

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Investigating Pascal's Triangle

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Sums of Powers - A Festive Story

Stage: 3 and 4

A story for students about adding powers of integers - with a festive twist.

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Tables Without Tens

Stage: 2 Challenge Level: Challenge Level:1

Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.

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Squares, Squares and More Squares

Stage: 3 Challenge Level: Challenge Level:1

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?

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Polite Numbers

Stage: 5 Challenge Level: Challenge Level:1

A polite number can be written as the sum of two or more consecutive positive integers. Find the consecutive sums giving the polite numbers 544 and 424. What characterizes impolite numbers?

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Cherries Come in Twos

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Six in a Circle

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

If there is a ring of six chairs and thirty children must either sit on a chair or stand behind one, how many children will be behind each chair?

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Transformations Tables

Stage: 2 Challenge Level: Challenge Level:1

These grids are filled according to some rules - can you complete them?

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Red Balloons, Blue Balloons

Stage: 2 Challenge Level: Challenge Level:1

Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?

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Series Sums

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Natural Sum

Stage: 4 Challenge Level: Challenge Level:1

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. . . .

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Summats Clear

Stage: 5 Challenge Level: Challenge Level:1

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.

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Janusz Asked

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

In y = ax +b when are a, -b/a, b in arithmetic progression. The polynomial y = ax^2 + bx + c has roots r1 and r2. Can a, r1, b, r2 and c be in arithmetic progression?

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Be Reasonable

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Skip Counting

Stage: 1 Challenge Level: Challenge Level:1

Find the squares that Froggie skips onto to get to the pumpkin patch. She starts on 3 and finishes on 30, but she lands only on a square that has a number 3 more than the square she skips from.

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Alphabet Blocks

Stage: 1 and 2 Challenge Level: Challenge Level:1

These alphabet bricks are painted in a special way. A is on one brick, B on two bricks, and so on. How many bricks will be painted by the time they have got to other letters of the alphabet?

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The Great Tiling Count

Stage: 2 Challenge Level: Challenge Level:1

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.

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Doplication

Stage: 2 Challenge Level: Challenge Level:1

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

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Matchsticks

Stage: 2 Challenge Level: Challenge Level:1

Reasoning about the number of matches needed to build squares that share their sides.