Arithmetic sequences

problem
Transformations tables

Age

7 to 11

Challenge level

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

Age

14 to 16

Challenge level

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

Age

16 to 18

Challenge level

What can you say about the common difference of an AP where every term is prime?
problem
Natural sum

Age

14 to 16

Challenge level

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.
problem
Summats clear

Age

16 to 18

Challenge level

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.
problem
Days and dates

Age

11 to 14

Challenge level

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
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
Be reasonable

Age

16 to 18

Challenge level

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

Age

5 to 7

Challenge level

Find the next two dominoes in these sequences.