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Broad Topics >

Sequences, Functions and Graphs > Arithmetic sequence

##### Stage: 5 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.

##### Stage: 3 and 4

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

##### Stage: 5 Challenge Level:

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

##### Stage: 5 Challenge Level:

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

##### Stage: 4 Challenge Level:

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

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

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

##### Stage: 4 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. . . .

##### Stage: 4 Challenge Level:

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

##### Stage: 5 Challenge Level:

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?

##### Stage: 4 Challenge Level:

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?

##### Stage: 5 Challenge Level:

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

##### Stage: 4 Challenge Level:

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

##### Stage: 3 and 4 Challenge Level:

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