Write the following series in sigma notation.
2, plus, 5, plus, 8, plus, 11, plus, 14, plus, 17
2+5+8+11+14+17

The given series is an arithmetic sequence where the first term \( a_1 = 2 \) and the common difference \( d = 3 \).

To express this series in sigma notation, we need to write the general term of the sequence. The general term for an arithmetic sequence is:

\[
a_n = a_1 + (n-1)d
\]

Substituting the values \( a_1 = 2 \) and \( d = 3 \):

\[
a_n = 2 + (n-1)3 = 3n - 1
\]

Now, express the series using sigma notation. The series has 6 terms, so the sum can be written as:

\[
\sum_{n=1}^{6} (3n - 1)
\]

This is the sigma notation for the series.

Would you like more details or have any questions?

Here are 5 relative questions for practice:
1. How would you write a similar series with a common difference of 5 in sigma notation?
2. How would the sigma notation change if the series had 10 terms instead of 6?
3. Can you find the sum of the first 10 terms of the arithmetic sequence with the same rule \(3n - 1\)?
4. How do you calculate the sum of an arithmetic series using a different method?
5. How can you identify the common difference in a sequence if it's not given?

**Tip:** For arithmetic series, the common difference between terms is key to identifying patterns and writing the series in sigma notation.

Write the following series in sigma notation: 2 + 5 + 8 + 11 + 14 + 17

Learn how to express the arithmetic series 2 + 5 + 8 + 11 + 14 + 17 in sigma notation. This solution covers the key concepts of arithmetic sequences, including the general term formula and how to use sigma notation to represent a series. Suitable for students in Grades 8-10.

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