Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 14 - Sequences, Series, and the Binomial Theorem - Review Exercises: Chapter 14 - Page 927: 1

Answer

False statement

Work Step by Step

Sequence $10,15,20,\ldots $ The general term or ${{n}^{th}}$ term of the arithmetic sequence is ${{a}_{n}}$. and ${{a}_{n}}={{a}_{1}}+\left( n-1 \right)d$ Where, ${{a}_{1}}$ is the first term and $d$ is the difference between the consecutive terms (common difference). Here ${{a}_{1}}=10$ And $d={{a}_{n+1}}-{{a}_{n}}$ $\begin{align} & d={{a}_{n+1}}-{{a}_{n}} \\ & ={{a}_{1+1}}-{{a}_{1}} \\ & ={{a}_{2}}-{{a}_{1}} \end{align}$ Put ${{a}_{1}}=10$ and ${{a}_{2}}=15$ $\begin{align} & d={{a}_{2}}-{{a}_{1}} \\ & =15-10 \\ & =5 \end{align}$ Next term of the given sequence $10,15,20,\ldots $is ${{4}^{th}}$ term $\begin{align} & {{a}_{4}}={{a}_{1}}+\left( 4-1 \right)d \\ & =10+3\times 5 \\ & =10+15 \\ & =25 \end{align}$ Thus, the next term in the arithmetic sequence $10,15,20,\ldots $ is 25. Therefore, the given statement β€˜The next term in the arithmetic sequence $10,15,20,\ldots $ is 35’ is false.
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