Numbers

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.