## Intermediate Algebra for College Students (7th Edition)

$\sum_{i=1}^{14}(2i+3)$
Since, we have $5+7+9+11+.....31$ This form an arithmetic progression sequence whose first term is $5$ and last term is $31$ with common difference of $2$. For an arithmetic progression sequence, we have $a_n=a_1+(n-1)d$ thus, $a_n=5+(n-1)2=5+2n-2=2n+3$ when $n=14$ Lat term becomes $a_{14}=2(14)+3=31$ Hence, $5+7+9+11+.....31$can be summed up with the summation notation as: $\sum_{i=1}^{14}(2i+3)$