Question: My daughter had me help her with some of her college math problems that require finding the pattern. The problem was the stair problem where you can climb either 1 step or 2 steps at a time. How many combinations are there to get to the 10th step. I found the data set that solves the answer to the question, but is there an equation that expresses the answer in terms of n?

1 2 3 4 5 6 7 8 9 10 stair number
1 2 3 5 8 13 21 34 55 89 number of possible combinations

Hi Arnold,

Did you notice the pattern in these numbers. The first two are 1 and 2, and after that, each term is the sum of the previous two.

3 = 1 + 2, 5 = 2 + 3, 8 = 3 + 5, ...

This sequence is called the Fibonacci sequence after an Italian mathematician Leonordo Fibonacci (1170, 1250).

There is an explanation of why his sequence gives the number of possible combinations in your stair problem in a note that Denis wrote in 1995.

Harley