Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 10 - Section 10.2 - Arithmetic Sequences - Concept and Vocabulary Check - Page 159: 3


The sum, ${{S}_{n}}$, of the first $ n $ terms of the sequence described in Exercise 1 is given by the formula ${{S}_{n}}$ = $\frac{n}{2}({{a}_{1}}+{{a}_{n}})$, where ${{a}_{1}}$ is the first term and ${{a}_{n}}$ is the nth term.

Work Step by Step

To find the sum of the first n terms, we need to have the first term of the sequence, the common difference and the number of terms of which sum is to be determined. The sum is denoted by ${{S}_{n}}$, the first term by ${{a}_{n}}$, the common difference by $ d $, and the number of terms by $ n $. Thus, the formula for determining the sum of the first n terms is given by, $\begin{align} & {{S}_{n}}=\frac{n}{2}\left( {{a}_{1}}+{{a}_{n}} \right) \\ & {{S}_{n}}=\frac{n}{2}\left\{ 2{{a}_{1}}+\left( n-1 \right)d \right\} \\ \end{align}$
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