what do you call indicated sum of sequences

The indicated sum of a sequence is called a **series**. Specifically, a series refers to the sum of the terms in a sequence, often written using summation notation (Σ). For example, if you have a sequence of terms \( a_1, a_2, a_3, \dots, a_n \), the indicated sum or series would be:

\[
S = a_1 + a_2 + a_3 + \dots + a_n = \sum_{i=1}^{n} a_i
\]

There are different types of series, such as:

1. **Finite series**: The sum of a finite number of terms.
2. **Infinite series**: The sum of an infinite sequence of terms.
3. **Arithmetic series**: The sum of the terms in an arithmetic sequence.
4. **Geometric series**: The sum of the terms in a geometric sequence.

Would you like further details or have any other questions?

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Here are five related questions to deepen your understanding:

1. What is the difference between a sequence and a series?
2. How do you calculate the sum of an arithmetic series?
3. What is the formula for the sum of a finite geometric series?
4. How do you determine if an infinite series converges?
5. What are some examples of real-world applications of series?

**Tip:** When working with summation notation, always pay attention to the limits of summation (the starting and ending values) to ensure correct calculations.

Discover how the indicated sum of a sequence, known as a series, is calculated using summation notation. This explanation covers finite and infinite series, arithmetic and geometric series, and essential formulas. Suitable for students in Grades 10-12.

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