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?
Prove that the sum of the reciprocals of the first n triangular numbers gets closer and closer to 2 as n grows.
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?
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.
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.
Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?
Use algebra to reason why 16 and 32 are impossible to create as the sum of consecutive numbers.