Answer:
[tex]S_{31}=71.3[/tex]
Step-by-step explanation:
The nth term of an arithmetic sequence is given by the formula,
[tex]U_n=a_1+(n-1)d[/tex]
We were given that the 9th term is [tex]17[/tex].
[tex]\Rightarrow 17=a_1+(9-1)(-2.1)[/tex]
[tex]\Rightarrow 17=a_1+(8)\times(-2.1)[/tex]
[tex]\Rightarrow 17=a_1-\frac{84}{5}[/tex]
[tex]\Rightarrow 17+\frac{84}{5}=a_1[/tex]
[tex]\Rightarrow a_1=\frac{169}{5}[/tex]
The sum of the first n-terms is given by the formula,
[tex]S_n=\frac{n}{2}(2a_1+(n-1)d)[/tex]
To find [tex]S_{31}[/tex], we substitute [tex]n=31[/tex], [tex]a_1=\frac{169}{5}[/tex] and [tex]d=-2.1[/tex].
[tex]\Rightarrow S_{31}=\frac{31}{2}(2(\frac{169}{5}+(31-1)(-2.1))[/tex]
[tex]\Rightarrow S_{31}=\frac{31}{2}(2(\frac{169}{5}+(30)(-2.1))[/tex]
[tex]\Rightarrow S_{31}=\frac{31}{2}(\frac{23}{5})[/tex]
[tex]\Rightarrow S_{31}=\frac{713}{10}[/tex]
[tex]\Rightarrow S_{31}=71.3[/tex]
The correct answer is D
