Given the sequence:
[tex]\frac{11}{5},\frac{8}{5},1,\frac{2}{5},...[/tex]We will check the type of the sequence arithmetic or geometric
[tex]\begin{gathered} \frac{8}{5}-\frac{11}{5}=-\frac{3}{5} \\ \\ 1-\frac{8}{5}=-\frac{3}{5} \\ \\ \frac{2}{5}-1=-\frac{3}{5} \end{gathered}[/tex]As shown there is a common difference = -3/5
So, it will be an arithmetic sequence.
We will find the sum of the first 16 terms using the following formula:
[tex]S=\frac{n}{2}(2a+(n-1)d)[/tex]Substitute n = 16, d = -3/5, and a = 11/5
[tex]S=\frac{16}{2}(2*\frac{11}{5}+(16-1)(-\frac{3}{5}))=-36\frac{4}{5}=-36.8[/tex]So, the answer will be option c) -36.8
