To find the sum of an arithmetic sequence up to the nth term, we use the sum formula, which is
[tex]S_n=n(\frac{a_1+a_n}{2})[/tex]
where a1 represents the first term, and an the nth term.
The general term of our sequence is
[tex]a_n=3n+2[/tex]
We want to sum up to the 16th term. Evaluanting n = 16 and n = 1 on this expression, we get the terms to plug in our formula
[tex]\begin{gathered} a_1=3(1)+2=3+2=5 \\ a_{16}=3(16)+2=48+2=50 \end{gathered}[/tex]
Then, the sum is equal to
[tex]\sum_{i\mathop{=}1}^{16}(3i+2)=16(\frac{50+5}{2})=8\cdot55=440[/tex]
The result of this sum is 440.
