What is the sum of the finite arithmetic series? (-15)+0+15+30+...+195A. 1,355B. 1,350C. 1,335D. 1,000

The underlying arithmetic progression is-15, 0, 15, 30, ...starting with [tex]a_1=-15[/tex] and with a common difference of [tex]d=15[/tex] between terms. Recursively, this sequence is given by[tex]\begin{cases}a_1=-15\\a_n=a_{n-1}+15&\text{for }n>1\end{cases}[/tex]So we have[tex]a_2=a_1+15[/tex][tex]a_3=a_2+15=a_1+15\cdot2[/tex][tex]a_4=a_3+15=a_1+15\cdot3[/tex]and so on, so that the explicit rule for the sequence is[tex]a_n=a_1+15(n-1)=15n-30[/tex]for [tex]n\ge1[/tex].The series consists of 15 terms, since[tex]195=15n-30\implies15n=225\implies n=15[/tex]So we have[tex]-15+0+15+\cdots+195=\displaystyle\sum_{n=1}^{15}(15n-30)=15\cdot\frac{15\cdot16}2-30\cdot15=1350[/tex]and the answer would be B.