Answer
$6+14+24+36+50+66+84+104=384$.
Work Step by Step
We need to sum the first eight terms of the sequence whose general term is $a_{n}=n^{2}+5n$. This yields
$\sum\limits^{8}_{n=1}(n^{2}+5n)=[1^{2}+5(1)]+[2^{2}+5(2)]+[3^{2}+5(3)]+[4^{2}+5(4)]+[5^{2}+5(5)]+[6^{2}+5(6)]+[7^{2}+5(7)]+[8^{2}+5(8)]$
$=6+14+24+36+50+66+84+104$
$=384$
