Answer
$a_n=n \sqrt 2$
and $a_{51} =51 \sqrt 2$
Work Step by Step
The $n^{th}$ term of an arithmetic sequence is given by the formula:
$a_n = a_1 + (n-1)d (1)$
where $a_1 = \ First \ Term; \\ d = \ Common \ Difference$
We have: $a_1=\sqrt 2 \\ d=\sqrt 2$
Next, we will substitute the above data into formula (1) to obtain:
$a_n=\sqrt 2+(\sqrt 2) (n-1) \implies a_n=n \sqrt 2$
In order to compute the $51st$ term, we need to plug in $51$ for $n$ into the above form to obtain:
$a_{51} = (51) \sqrt 2$
So, $a_{51} =51 \sqrt 2$
