Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 12 - Section 12.2 - Arithmetic Sequences - 12.2 Exercises - Page 857: 61



Work Step by Step

See p. 855. For the arithmetic sequence $a_{n}=a+(n-1)d$ the nth partial sum $S_{n}=\displaystyle \sum_{k=1}^{n}[a+(k-1)d]$ is given by either of the following equivalent formulas: 1. $S_{n}=\displaystyle \frac{n}{2}[2a+(n-1)d]\qquad $2. $S_{n}=n(\displaystyle \frac{a+a_{n}}{2})$ ------------------- We see from the given sequence that $a=0.7$ $d=2.7-0.7=2$ The last term is $a_{n}=56.7$ (we find n): $a_{n}=a+(n-1)d$ $56.7=0.7+2(n-1)\qquad/-0.7$ $56=2(n-1)\qquad/\div 2$ $28=n-1$ $29=n$ Finally, we find $S_{29}$, (using formula 2) $S_{29}=29(\displaystyle \frac{0.7+56.7}{2})=832.3$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.