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What is the summation notation for the arithmetic series? Enter the correct values for [tex]x[/tex], [tex]y[/tex], and [tex]z[/tex].

[tex]\[ \sum_{k=1}^x(y + zk) \][/tex]

[tex]\[ x = \square \][/tex]
[tex]\[ y = \square \][/tex]
[tex]\[ z = \square \][/tex]

Sagot :

GinnyAnswer
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]
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