Find each sum. 1+3+5+⋯+59

Name: Problem 44, Chapter 11: Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry
Uploaded: 2020-05-09T01:50:07-08:00
Duration: 1 min 46 s
Channel: Julie Silva
Description: Find each sum. 1+3+5+⋯+59

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Key Concepts

Arithmetic Sequence

An arithmetic sequence is a list of numbers where each term after the first is obtained by adding a constant difference to the preceding term. This concept is key in understanding sequences that progress by consistent increments, allowing for the prediction of future terms and facilitating various calculation techniques in algebra.

Arithmetic Series Sum Formula

The arithmetic series sum formula is a method used to calculate the sum of the terms in an arithmetic sequence without having to add each term individually. Typically expressed as S = n/2 * (first term + last term) or S = n/2 * (2a + (n-1)d), where n is the number of terms, this formula simplifies the process of summing sequences with a constant difference.

Finding the Number of Terms

Determining the number of terms in an arithmetic sequence is crucial when applying the series sum formula. This involves using the general term formula, a_n = a_1 + (n-1)d, where a_n represents the nth term, a_1 the first term, and d the common difference. By solving for n when the last term is known, one can accurately compute the total number of terms in the sequence.

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