Eccoci.

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:

\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}

The $12$th 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?