Resources tagged with: Arithmetic sequences
There are 49 NRICH Mathematical resources connected to Arithmetic sequences, you may find related items under Patterns, sequences and structure.
Broad Topics > Patterns, sequences and structure > Arithmetic sequences
Growing Surprises
Can you find the connections between linear and quadratic patterns?
What Numbers Can We Make Now?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Seven Squares
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
Steel Cables
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
Odds, Evens and More Evens
Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...
What Numbers Can We Make?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Charlie's Delightful Machine
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
A Little Light Thinking
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
Shifting Times Tables
Can you find a way to identify times tables after they have been shifted up or down?
Slick Summing
Watch the video to see how Charlie works out the sum. Can you adapt his method?
Mystic Rose
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
Elevenses
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Multiplication Square Jigsaw
Can you complete this jigsaw of the multiplication square?
Squares in Rectangles
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?
Coordinate Patterns
Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
Seven Squares - Group-worthy Task
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
More Number Pyramids
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Proof Sorter - Sum of an Arithmetic Sequence
Put the steps of this proof in order to find the formula for the sum of an arithmetic sequence
Prime AP
What can you say about the common difference of an AP where every term is prime?
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...
Missing Middles
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 three dominoes?
Buzzy Bee
Buzzy Bee was building a honeycomb. She decorated the honeycomb with a pattern using numbers. Can you discover Buzzy's pattern and fill in the empty cells for her?
Doplication
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?
Maxagon
What's the greatest number of sides a polygon on a dotty grid could have?
Speedy Summations
Watch the video to see how to add together an arithmetic sequence of numbers efficiently.
Prime Sequences
This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?
Mobile Numbers
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?
Investigating Pascal's Triangle
In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.
Tables Without Tens
Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.
Unravelling Sequences
Can you describe what is happening as this program runs? Can you unpick the steps in the process?
Squares, Squares and More Squares
Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?
Polite Numbers
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?
Cherries Come in Twos
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?
Six in a Circle
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?
Transformations Tables
These grids are filled according to some rules - can you complete them?
Red Balloons, Blue Balloons
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?
Series Sums
Let S1 = 1 , S2 = 2 + 3, S3 = 4 + 5 + 6 ,........ Calculate S17.
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.
Summats Clear
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.
Janusz Asked
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?
Be Reasonable
Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.
Skip Counting
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.
Alphabet Blocks
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?
The Great Tiling Count
Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.
Matchsticks
Reasoning about the number of matches needed to build squares that share their sides.