Given:
The sequence is: -3, -1, 1, 3,..
Required: The sum of the first 85 terms
The sequence is a an arithmetic progression where:
first term (a) = -3
common difference (d) = 2
The formula for the sum of the first n terms of an arithmetic progression is:
[tex]S_n=\text{ }\frac{n}{2}[2a\text{ + \lparen n-1\rparen d\rbrack}[/tex]For this problem, n = 85
Substituting the given values:
[tex]\begin{gathered} S_{85}\text{ = }\frac{85}{2}[2\times-3\text{ + \lparen85-1\rparen}\times2] \\ =\text{ 6885} \end{gathered}[/tex]Answer: Option C
