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.
This group tasks allows you to search for arithmetic progressions
in the prime numbers. How many of the challenges will you discover
A story for students about adding powers of integers - with a festive twist.
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
Cellular is an animation that helps you make geometric sequences
composed of square cells.
Watch the video to see how to add together an arithmetic sequence of numbers efficiently.
Watch the video to see how Charlie works out the sum. Can you adapt his method?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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?
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
Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic
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?
Let S1 = 1 , S2 = 2 + 3, S3 = 4 + 5 + 6 ,........ Calculate S17.
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. . . .
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?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Investigate how you can work out what day of the week your birthday
will be on next year, and the year after...