Given the following series:
[tex]-33,-27,-21,-15,....[/tex]We will write the sigma notation for the given series
the given series is an arithmetic series becuase there is a common difference=6
we will find the explicit formula of the arithmetic series
[tex]a_n=a+d(n-1)[/tex]Substitute a = -33, d = 6
[tex]a_n=-33+6(n-1)[/tex]Simplify the expression:
[tex]\begin{gathered} a_n=-33+6n-6 \\ a_n=6n-39 \end{gathered}[/tex]The sigma notation for the infinite series will be as follows:
[tex]\sum_{n\mathop{=}1}^{\infty}(6n-39)[/tex]So, the answer will be:
[tex]\sum_{n\mathop{=}1}^{\infty}(6n-39)[/tex]