To express the summation notation for an arithmetic series, we generally use the form:
[tex]\[
\sum_{k=1}^x(y + zk)
\][/tex]
Given the structure of the problem, let's determine the specific values of [tex]\( x \)[/tex], [tex]\( y \)[/tex], and [tex]\( z \)[/tex].
- The series has [tex]\( x = 10 \)[/tex] terms.
- The starting number of the series is [tex]\( y = 7 \)[/tex].
- The common difference between consecutive terms in the series is [tex]\( z = 4 \)[/tex].
So, we can fill in the blanks as follows:
[tex]\[
\begin{array}{l}
\sum_{k=1}^x(y + z k) \\
x = 10
\end{array}
\][/tex]
[tex]\[
y = 7
\][/tex]
[tex]\[
z = 4
\][/tex]
Thus, the summation notation and the values are:
[tex]\[
\sum_{k=1}^{10}(7 + 4k)
\][/tex]
