Question

Find the sum of the first 14 terms of each arithmetic sequence. $$-8,-5,-2,1,4, \dots$$

   Find the sum of the first 14 terms of each arithmetic sequence.
$$-8,-5,-2,1,4, \dots$$

Precalculus : Building Concepts and Connections

Precalculus : Building Concepts and Connections

Revathi Narasimhan 1st Edition

Chapter 10, Problem 8

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Solved by Expert Tony Ni

04/14/2020

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In this case, the first term a is -8 and the common difference d is 3 (since each term increases by 3 from the previous term). Show more…

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Find the sum of the first 14 terms of each arithmetic sequence. $$-8,-5,-2,1,4, \dots$$

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Key Concepts

Arithmetic Sequence

An arithmetic sequence is a sequence of numbers where each term is obtained by adding a constant difference to the previous term. This constant, called the common difference, distinguishes arithmetic sequences from other types of sequences, and allows for predictable patterns and behaviors in the sequence's progression.

Nth Term Formula

The nth term of an arithmetic sequence can be found using the formula: a_n = a_1 + (n - 1)d, where a_1 is the first term, d is the common difference, and n is the term number. This formula is essential for determining any specific term within the sequence when the first term and the common difference are known.

Sum of an Arithmetic Series

The sum of the first n terms of an arithmetic sequence, also called an arithmetic series, can be calculated using the formula: S_n = n/2 * (a_1 + a_n) or equivalently S_n = n/2 * (2a_1 + (n - 1)d). This formula is important for quickly computing the total of all terms up to a certain point in the sequence without having to add each term individually.

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