Write the following series in sigma notation.
3, plus, 11, plus, 19, plus, 27, plus, 35, plus, 43, plus, 51
3+11+19+27+35+43+51

The given series is:

\[ 3 + 11 + 19 + 27 + 35 + 43 + 51 \]

This is an arithmetic series where the first term \(a = 3\) and the common difference \(d = 8\). To express this series in sigma notation, we need to write it as a summation of terms that follow the arithmetic progression formula:

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

Where:
- \(a = 3\) (the first term),
- \(d = 8\) (the common difference).

The series has 7 terms, so \(n\) will range from 1 to 7.

Thus, in sigma notation, the series is:

\[
\sum_{n=1}^{7} \left( 3 + (n-1) \cdot 8 \right)
\]

This represents the sum of the arithmetic sequence starting from 3 and increasing by 8 each time for 7 terms.

Would you like more details, or have any questions?

Here are 5 related questions:
1. How do you calculate the sum of an arithmetic series?
2. What is the general formula for the \(n\)-th term of an arithmetic sequence?
3. How would the sigma notation change if the common difference were negative?
4. Can you express a geometric series in sigma notation?
5. What is the relationship between sigma notation and integrals?

**Tip:** In an arithmetic sequence, the difference between any two consecutive terms remains constant, making it easy to identify and express using summation formulas.

Write the following series in sigma notation. 3+11+19+27+35+43+51

Learn how to express the arithmetic series 3 + 11 + 19 + 27 + 35 + 43 + 51 in sigma notation. This problem covers important concepts like arithmetic sequences and summation using sigma notation. Suitable for students in Grades 8-10.

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