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