Discover and prove how different number sequences combine to create other sequences.
Hook showing the sum of consecutive odd numbers equals a perfect square.
1 = 1
1 + 3 = 4
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16
1 + 3 + 5 + 7 + 9 = 25
Explanation of adding counting numbers up and down to get squares.
Did you know there's another beautiful way to build square numbers using counting numbers?
Instead of adding odd numbers, try adding numbers up to a peak and then back down!
Let's test this out:
Question asking for the sum of the first 10 and 100 odd numbers.
By imagining the picture of nested squares, what is the sum of the first 100 odd numbers?
3 attempts remaining
Diamond dot pattern showing the up and down addition.
Count the number of dots in each row and add them together. This sum results in a square number:
Summary grid of other strange sequence transformations.