Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.
This group tasks allows you to search for arithmetic progressions in the prime numbers. How many of the challenges will you discover for yourself?
Watch the video to see how to add together an arithmetic sequence of numbers efficiently.
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.
Put the steps of this proof in order to find the formula for the sum of an arithmetic sequence
What can you say about the common difference of an AP where every term is prime?
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?
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. . . .
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
Watch the video to see how Charlie works out the sum. Can you adapt his method?
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.