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 - Exercise Set - Page 1060: 62

Answer

a) ${{a}_{n}}=0.3n+24.1$. b) $33.1\%$

Work Step by Step

(a) The general equation of the nth term is given by ${{a}_{n}}={{a}_{1}}+\left( n-1 \right)d $. So, $\begin{align} & {{a}_{n}}={{a}_{1}}+\left( n-1 \right)d \\ & {{a}_{n}}=24.4+\left( n-1 \right)0.3 \\ & {{a}_{n}}=24.4+0.3n-0.3 \\ & {{a}_{n}}=0.3n+24.1 \\ \end{align}$ (b) We use $ n=30$ because after 1989 until 2019, 30 years pass. So, $\begin{align} & {{a}_{n}}=0.3n+24.1 \\ & {{a}_{n}}=0.3\left( 30 \right)+24.1 \\ & {{a}_{n}}=33.1 \\ \end{align}$
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