Write the following series in sigma notation.
2, plus, 11, plus, 20, plus, 29, plus, 38, plus, 47, plus, 56
2+11+20+29+38+47+56\

The given series is:

\[
2 + 11 + 20 + 29 + 38 + 47 + 56
\]

This is an arithmetic sequence where the first term \(a = 2\) and the common difference \(d = 9\).

In general, the \(n\)-th term of an arithmetic sequence is given by:

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

For this sequence:
\[
a_n = 2 + (n - 1) \cdot 9 = 9n - 7
\]

The series can be written in sigma notation as:

\[
\sum_{n=1}^{7} (9n - 7)
\]

This represents the sum of the first 7 terms of the arithmetic sequence.

Would you like more details or have any questions about this?

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Here are 5 related questions:
1. How do you find the common difference in an arithmetic sequence?
2. What is the formula for the sum of an arithmetic series?
3. How do you calculate the sum of an infinite arithmetic sequence?
4. Can you convert this sigma notation into a closed-form expression?
5. How do arithmetic sequences differ from geometric sequences?

**Tip**: In an arithmetic sequence, the common difference is constant between consecutive terms!

Write the following series in sigma notation: 2 + 11 + 20 + 29 + 38 + 47 + 56

Learn how to express the arithmetic series 2 + 11 + 20 + 29 + 38 + 47 + 56 in sigma notation. This step-by-step explanation covers the general formula for arithmetic sequences and how to use sigma notation to represent series. Ideal for students in Grades 9-10.

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