pls help

2.

Recall that a Fibonacci sequence is one in which all entries from the third onward are the sum of the two entries before it.
If the 5th and 8th entries of a Fibonacci Sequence are 19 and 79,
respectively, then what is the first entry of this sequence?

$\begin{array}{|lrcll|} \hline & a_5 &=& 19 \\ & a_8 &=& 79 \\ \hline &\mathbf{ a_6+a_7} &=& \mathbf{a_8} \\ (1) & a_6+a_7 &=& 79 \\ \hline &\mathbf{ a_5+a_6} &=& \mathbf{a_7} \\ (2)& 19+a_6 &=& a_7 \\ \hline (1)+(2): & 19+2a_6+a_7 &=& 79+a_7 \\ &19 + 2a_6 &=& 79 \\ & 2a_6 &=& 79-19 \\ &2a_6 &=& 60 \quad &| \quad : 2 \\ & \mathbf{a_6} &=& \mathbf{30} \\ \hline \end{array}$

$\begin{array}{|rcll|} \hline a_4+a_5 &=& a_6 \\ a_4 + 19 &=& 30 \\ \mathbf{a_4} &=& \mathbf{11} \\ \hline a_3+a_4 &=& a_5 \\ a_3 + 11 &=& 19 \\ \mathbf{a_3} &=& \mathbf{8} \\ \hline a_2+a_3 &=& a_4 \\ a_2 + 8 &=& 11 \\ \mathbf{a_2} &=& \mathbf{3} \\ \hline a_1+a_2 &=& a_3 \\ a_1 + 3 &=& 8 \\ \mathbf{a_1} &=& \mathbf{5} \\ \hline \end{array}$

1/1300  =  1/13 *  ( 1/100)  =  .00076923

The part in red is the repeating part with a period of 6

So

When  n  = 16

2 + 6 (16)  =  2 + 96  = 98 digits  to the right of the decimal point

So....the 100th digit will be the second digit in the period  =  7