statement.html
problem 25 · 21 lines
<div class="problem_content" role="problem">
<p>The Fibonacci sequence is defined by the recurrence relation:</p>
<blockquote>$F_n = F_{n - 1} + F_{n - 2}$, where $F_1 = 1$ and $F_2 = 1$.</blockquote>
<p>Hence the first $12$ terms will be:</p>
$$\begin{align}
F_1 &= 1\\
F_2 &= 1\\
F_3 &= 2\\
F_4 &= 3\\
F_5 &= 5\\
F_6 &= 8\\
F_7 &= 13\\
F_8 &= 21\\
F_9 &= 34\\
F_{10} &= 55\\
F_{11} &= 89\\
F_{12} &= 144
\end{align}$$
<p>The $12$th term, $F_{12}$, is the first term to contain three digits.</p>
<p>What is the index of the first term in the Fibonacci sequence to contain $1000$ digits?</p>
</div>