Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.2 Arithmetic Sequences - 12.2 Assess Your Understanding - Page 814: 45



Work Step by Step

We have to determine the sum: $S=5+9+13+.....+49$ As $9-5=13-9=...=4$, the sequence is arithmetic. Determine its first term and the common difference: $a_1=5$ $d=4$ The terms can be written as: $5=4\cdot 1+1$ $9=4\cdot 2+1$ $13=4\cdot 3+1$ .............................. $49=4\cdot 12+1$ Therefore, the given sum contains $12$ terms, so we have to determine the sum of the first $12$ terms. We use the formula: $S_n=\dfrac{n(a_1+a_n)}{2}$ $5+9+13+...+49=\dfrac{12(5+49)}{2}$ $=\dfrac{12\cdot 54}{2}$ $=324$
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