What’s next in the sequence 1, 11, 121, 1331?

January 2, 2015 — 2 Comments

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. And if you want to know more, the best explanation is here.

2 responses to What’s next in the sequence 1, 11, 121, 1331?

  1. 

    1 5 10 10 5 1

    • 

      Hi Vishal, nice one, you got the 6th row of Pascal’s triangle. Incidentally, to convert it into the necessary power of 11, we need to remember that each digit represents a place value. So, working from the right, 11^5 would work out to be:
      units digit: 1
      tens digit: 5
      hundreds digit: 0, carry 1
      thousands digit: 10 + the carried 1 = 11, so 1, carry 1
      ten thousands digit: 5 + the carried 1 = 6
      hundred thousands digit: 1

      So 11^5 = 161051

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