Arithmetic sequences

problem

Mobile Numbers

Age

5 to 11

Challenge level

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?
problem

Be Reasonable

Age

16 to 18

Challenge level

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

Janusz Asked

Age

16 to 18

Challenge level

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?
problem

Series Sums

Age

14 to 16

Challenge level

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

Skip Counting

Age

5 to 7

Challenge level

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.
problem

Six in a Circle

Age

5 to 7

Challenge level

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?
problem

Alphabet Blocks

Age

5 to 11

Challenge level

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?
problem

The Great Tiling Count

Age

7 to 11

Challenge level

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

Red Balloons, Blue Balloons

Age

7 to 11

Challenge level

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?
problem

Tables Without Tens

Age

7 to 11

Challenge level

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