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: 46



Work Step by Step

We have to determine the sum: $S=2+5+8+.....+41$ As $5-2=8-5=...=3$, the sequence is arithmetic. Determine its first term and the common difference: $a_1=2$ $d=3$ The terms can be written as: $2=3\cdot 1-1$ $5=3\cdot 2-1$ $8=3\cdot 3-1$ .............................. $41=3\cdot 14-1$ Therefore, the given sum contains $14$ terms, so we have to determine the sum of the first $14$ terms. We use the formula: $S_n=\dfrac{n(a_1+a_n)}{2}$ $2+5+8+...+41=\dfrac{14(2+41)}{2}$ $=\dfrac{14\cdot 43}{2}$ $=301$
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