Watch the video to see how to add together an arithmetic sequence of numbers efficiently.
Prove that the sum of the reciprocals of the first n triangular numbers gets closer and closer to 2 as n grows.
Watch the video to see how Charlie works out the sum. Can you adapt his method?
Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?
Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?
Can you find a rule which connects consecutive triangular numbers?
Can you find a rule which relates triangular numbers to square numbers?
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
Let S1 = 1 , S2 = 2 + 3, S3 = 4 + 5 + 6 ,........ Calculate S17.
Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.
Show that all pentagonal numbers are one third of a triangular number.
Use algebra to reason why 16 and 32 are impossible to create as the sum of consecutive numbers.