Write the following series in sigma notation.
2, plus, 12, plus, 22, plus, 32, plus, 42
2+12+22+32+42
Answer
Attempt 1 out of 2

The series you're working with is: 
\[
2 + 12 + 22 + 32 + 42
\]

This is an arithmetic sequence where the first term (\(a_1\)) is 2, and the common difference (\(d\)) is 10.

The general formula for the \(n\)-th term of an arithmetic sequence is:
\[
a_n = a_1 + (n - 1)d
\]

So, for this series:
\[
a_n = 2 + (n - 1) \cdot 10 = 10n - 8
\]

Now, we can express the series in sigma notation:
\[
\sum_{n=1}^{5} (10n - 8)
\]

This represents the sum of the terms from \(n = 1\) to \(n = 5\) of the arithmetic sequence, matching the given series.

Would you like a breakdown of any step? 

### Related questions:
1. How do you find the sum of an arithmetic series?
2. What is the general formula for an arithmetic sequence?
3. How does the common difference affect the series?
4. Can you convert a different arithmetic series to sigma notation?
5. How does sigma notation work for geometric series?

### Tip:
Always check if the sequence is arithmetic (constant difference) or geometric (constant ratio) before writing in sigma notation.

Write the following series in sigma notation: 2 + 12 + 22 + 32 + 42

Learn how to express the arithmetic sequence 2 + 12 + 22 + 32 + 42 in sigma notation. This problem covers key mathematical concepts, including arithmetic sequences, the general term formula, and sigma notation. Suitable for students in Grades 9-11.

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