Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 11 - 11.2 - Arithmetic Sequences and Partial Sums - 11.2 Exercises - Page 786: 9


It is an arithmetic sequence. $d=\frac{1}{4}$

Work Step by Step

A sequence is arithmetic if $a_2−a_1=a_3−a_2=a_4−a_3=a_5−a_4=...=d$ For the given sequence we have that: $a_2-a_1=\frac{3}{2}-\frac{5}{4}=\frac{3(2)}{2(2)}-\frac{5}{4}=\frac{6}{4}-\frac{5}{4}=\frac{1}{4}$ $a_3-a_2=\frac{7}{4}-\frac{3}{2}=\frac{7}{4}-\frac{3(2)}{2(2)}=\frac{7}{4}-\frac{6}{4}=\frac{1}{4}$ $a_4-a_3=2-\frac{7}{4}=\frac{2(4)}{4}-\frac{7}{4}=\frac{8}{4}-\frac{7}{4}=\frac{1}{4}$ $a_5-a_4=\frac{9}{4}-2=\frac{9}{4}-\frac{2(4)}{4}=\frac{9}{4}-\frac{8}{4}=\frac{1}{4}$ It is an arithmetic sequence. Common difference: $d=\frac{1}{4}$
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.