The formula to find the sum of the first n-terms in an arithmetic series is:
[tex]S_n=\frac{n(a_1+a_n)}{2}[/tex]
Where n is the number of terms, a1 is the first term and an is the last term.
Now, we know a1=2 and the common difference is d=2, with this information we can find a16 by using the following formula:
[tex]a_n=a_1+(n-1)d[/tex]
Then, replace n=16, a1=2 and d=2 and solve:
[tex]\begin{gathered} a_{16}=2+(16-1)\cdot2 \\ a_{16}=2+15\cdot2 \\ a_{16}=2+30 \\ a_{16}=32 \end{gathered}[/tex]
Now replace this value into the formula of the sum and solve:
[tex]\begin{gathered} S_{16}=\frac{16\cdot(2+32)}{2} \\ S_{16}=\frac{16\cdot(34)}{2} \\ S_{16}=\frac{544}{2} \\ S_{16}=272 \end{gathered}[/tex]
The answer is D. 272
