Consider the following sequence:

$\{\frac{1}{n^4}+1{\}}_n=1^{}$

Denoting the terms in the sequence by $a_n,$ enter the first $5$ such terms below.

Enter the exact answers.

$a_1=$

$a_2=$

$a_3=$

$a_4=$

$a_5=$

From your answers above, conjecture what number the sequence seems to settle to