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.