Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 9 - Conic Sections, Sequences, and Series - 9.3 Arithmetic Sequences - 9.3 Exercises - Page 728: 45

Answer

The sequence is arithmetic. Common difference: $d=6$. General term: $a_{n}=6n-2$.

Work Step by Step

$10-4=16-10=22-16=28-22=34-28=6$ We see that the difference between each term and the preceding term is same and is equal to $6$. Therefore, the sequence is arithmetic with common difference $d=6$. The general term $a_{n}$ is given by $a_{n}=a_{1}+(n-1)d$ As $a_1=4$ and $d=6$, the general term is: $a_{n}=4+(n-1)6=4+6n-6$ $a_{n}=6n-2$
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