Write the following series in sigma notation.
4, plus, 14, plus, 24, plus, 34, plus, 44
4+14+24+34+44

The given series is:  
\( 4 + 14 + 24 + 34 + 44 \)

To write this series in sigma notation, we first observe that it increases by a constant difference of 10 between consecutive terms. The first term is 4, and the common difference is 10.

We can express the terms of the series using the formula for the \(n\)-th term of an arithmetic sequence:
\[
a_n = 4 + (n-1) \cdot 10
\]

Now, to write the series in sigma notation, we can sum the terms from \(n = 1\) to \(n = 5\) (since there are 5 terms):

\[
\sum_{n=1}^{5} \left[ 4 + (n-1) \cdot 10 \right]
\]

Thus, the sigma notation for the series is:
\[
\sum_{n=1}^{5} (4 + (n-1) \cdot 10)
\]

Would you like further details or explanations?

Here are 5 related questions to expand on the topic:
1. How do you find the sum of an arithmetic series?
2. Can the same series be written using a different index?
3. What is the general formula for the sum of the first \(n\) terms of an arithmetic sequence?
4. How can we verify the sum of this series using the sigma notation?
5. How does the common difference affect the series?

**Tip:** In an arithmetic sequence, the difference between consecutive terms remains constant throughout the series.

Write the following series in sigma notation: 4, 14, 24, 34, 44

Learn how to express the arithmetic series 4, 14, 24, 34, 44 in sigma notation. This problem covers the key concepts of arithmetic sequences and sigma notation, with step-by-step guidance on identifying the general term and writing the series in summation form. Suitable for students in Grades 9-10.

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