Answer
$a_{80} =140\sqrt 5$
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: $a_1=2 \sqrt 5 \\ d=a_2-a_1=4 \sqrt 5-2 \sqrt 5=2 \sqrt 5$
We will substitute the above data into formula (1) to obtain:
$a_n=2 \sqrt 5+(2 \sqrt 5) (n-1)$
In order to compute the 80th term, we need to plug in $80$ for $n$ into the above form to obtain:
$a_{80} =2 \sqrt 5+(2 \sqrt 5) (80-1)=2\sqrt 5+138 \sqrt 5$
So, $a_{80} =140\sqrt 5$
