Sigma notation and evaluation of a finite sum

The sum of the first 5 terms in sigma notation is $\sum_{i=1}^{5} (3i-1).$ This means we plug in $i=1,2,3,4,5$ into $3i-1$ and add the results together.

Computing each term: $a_1=2$, $a_2=5$, $a_3=8$, $a_4=11$, $a_5=14$. Adding these gives $2+5+8+11+14 = 40$. Alternatively, using linearity, $\sum_{i=1}^{5}(3i-1) = 3\sum_{i=1}^{5} i - \sum_{i=1}^{5} 1 = 3(15) - 5 = 40$.