# Fibonacci Numbers

##### December 22, 2023

## Problem #

Given an integer n, find the nth Fibonacci number using dynamic programming. The first two Fibonacci numbers are 0 and 1, and each subsequent number is the sum of the previous two.

## Solution #

The Python code to find the nth Fibonacci number using dynamic programming is as follows:

```
def fibonacci(n):
# Initialize a list to store the Fibonacci numbers up to n
fib_sequence = [0, 1]
# Dynamic programming approach
for i in range(2, n + 1):
next_fib = fib_sequence[i - 1] + fib_sequence[i - 2]
fib_sequence.append(next_fib)
return fib_sequence[n]
# Example usage
n = 10 # for example, finding the 10th Fibonacci number
nth_fibonacci_number = fibonacci(n)
```

When this function is executed with `n = 10`

, it returns `55`

, which is the 10th number in the Fibonacci sequence.