Find each sum. 2+5+8+⋯+41

Name: Problem 46, Chapter 11: Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry
Uploaded: 2020-05-09T01:54:41-08:00
Duration: 1 min 49 s
Channel: Julie Silva
Description: Find each sum. 2+5+8+⋯+41

Key Concepts

Arithmetic Sequence

An arithmetic sequence is a sequence of numbers where each term after the first is obtained by adding a constant value, called the common difference, to the previous term. This type of sequence is fundamental because it provides a clear progression and can be analyzed using specific formulas for both individual terms and sums.

Common Difference

The common difference in an arithmetic sequence is the fixed amount that is added to each term to obtain the next term. It is an essential concept because it determines the pattern of the sequence and is used in calculating both individual terms and the overall sum of the sequence.

nth Term Formula

The nth term formula in an arithmetic sequence, typically expressed as a_n = a_1 + (n - 1) * d, provides a way to calculate any term by knowing the first term (a_1), the common difference (d), and the term's position (n). This formula is critical for identifying the properties of the sequence and solving related problems.

Sum of Arithmetic Series

The sum of an arithmetic series is the total of all terms in an arithmetic sequence. It is often calculated using the formula S_n = n/2 * (a_1 + a_n), where n is the number of terms, a_1 is the first term, and a_n is the last term. This concept is important because it allows for efficient computation of the sum without having to add each term individually.

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