Question

-33,-27,-21,-15....Write the sigma notation for the infinite series. ________________

Answer 1

Given the following series:

`-33,-27,-21,-15,....`

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

`a_n=a+d(n-1)`

Substitute a = -33, d = 6

`a_n=-33+6(n-1)`

Simplify the expression:

`\begin{gathered} a_n=-33+6n-6 \\ a_n=6n-39 \end{gathered}`

The sigma notation for the infinite series will be as follows:

`\sum_{n\mathop{=}1}^(\infty)(6n-39)`

So, the answer will be:

`\sum_{n\mathop{=}1}^(\infty)(6n-39)`