### There are 12 results

Broad Topics >

Numbers and the Number System > Triangle numbers

##### Age 16 to 18 Challenge Level:

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

##### Age 14 to 16 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

Prove that the sum of the reciprocals of the first n triangular numbers gets closer and closer to 2 as n grows.

##### Age 11 to 16 Challenge Level:

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?

##### Age 14 to 16 Challenge Level:

Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.

##### Age 14 to 16 Challenge Level:

Show that all pentagonal numbers are one third of a triangular number.

##### Age 14 to 16 Challenge Level:

Can you find a rule which connects consecutive triangular numbers?

##### Age 14 to 16 Challenge Level:

Can you find a rule which relates triangular numbers to square numbers?

##### Age 14 to 16 Challenge Level:

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

##### Age 14 to 16 Challenge Level:

Let S1 = 1 , S2 = 2 + 3, S3 = 4 + 5 + 6 ,........ Calculate S17.

##### Age 14 to 18 Challenge Level:

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

##### Age 14 to 16 Challenge Level:

Use algebra to reason why 16 and 32 are impossible to create as the
sum of consecutive numbers.