## 1000-digit Fibonacci number

### Problem 25

Published on Friday, 30th August 2002, 06:00 pm; Solved by 95028; Difficulty rating: 5%The Fibonacci sequence is defined by the recurrence relation:

F_{n}= F_{n−1}+ F_{n−2}, where F_{1}= 1 and F_{2}= 1.

Hence the first 12 terms will be:

F_{1}= 1

F_{2}= 1

F_{3}= 2

F_{4}= 3

F_{5}= 5

F_{6}= 8

F_{7}= 13

F_{8}= 21

F_{9}= 34

F_{10}= 55

F_{11}= 89

F_{12}= 144

The 12th term, F_{12}, is the first term to contain three digits.

What is the index of the first term in the Fibonacci sequence to contain 1000 digits?