Question: What’s the next number in the following sequence?
11, 121, 1331, …?
Answer
These are powers of 11. So the next number will be 11 x 11 x 11 x 11 = 14641.
The beautiful thing about the powers of 11 is that they follow Pascal’s triangle:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
You add the two numbers above to obtain the numbers below. Pascal’s triangle has a number of applications in probability, binomial expansions of brackets and geometry. It contains an incredible number of patterns within itself. Take a look and see what each row adds up to for a start!
If you want to know more, you can find a good explanation here.