data/problems/25.yml
---
:id: 25
:name: 1000-digit Fibonacci number
:url: https://projecteuler.net/problem=25
:content: "The Fibonacci sequence is defined by the recurrence relation:\n\n> F<sub><i>n</i></sub>
= F<sub><i>n</i>−1</sub> + F<sub><i>n</i>−2</sub>, where F<sub>1</sub> = 1 and F<sub>2</sub>
= 1.\n\nHence the first 12 terms will be:\n\n> F<sub>1</sub> = 1 \n> F<sub>2</sub>
= 1 \n> F<sub>3</sub> = 2 \n> F<sub>4</sub> = 3 \n> F<sub>5</sub> = 5 \n> F<sub>6</sub>
= 8 \n> F<sub>7</sub> = 13 \n> F<sub>8</sub> = 21 \n> F<sub>9</sub> = 34 \n>
F<sub>10</sub> = 55 \n> F<sub>11</sub> = 89 \n> F<sub>12</sub> = 144\n\nThe 12th
term, F<sub>12</sub>, is the first term to contain three digits.\n\nWhat is the
index of the first term in the Fibonacci sequence to contain 1000 digits?\n\n"