observe the following pattern, identify the variable and right the general expression 1,4,9,16,25
Answers
Surprising Patterns in the Square Numbers (1, 4, 9, 16…)
A quick puzzle for you — look at the first few square numbers:
1, 4, 9, 16, 25, 36, 49…
And now find the difference between consecutive squares:
1 to 4 = 3
4 to 9 = 5
9 to 16 = 7
16 to 25 = 9
25 to 36 = 11
…
Huh? The odd numbers are sandwiched between the squares?
Strange, but true. Take some time to figure out why — even better, find a reason that would work on a nine-year-old. Go on, I’ll be here.
Exploring Patterns
We can explain this pattern in a few ways. But the goal is to find a convincing explanation, where we slap our forehands with “ah, that’s why!”. Let’s jump into three explanations, starting with the most intuitive, and see how they help explain the others.
Geometer’s Delight
It’s easy to forget that square numbers are, well… square! Try drawing them with pebbles