College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 8, Sequences and Series - Section 8.2 - Arithmetic Sequences - 8.2 Exercises: 4

Answer

True

Work Step by Step

RECALL: The $n^{th}$ term $a_n$ of an arithmetic sequence can be found using the formula: $a_n=a+(n-1)d$ where $a$= first term $d$ = common difference\ $n$ = term number Thus, if you know the first two terms of an arithmetic sequence, the only required quantity in the formula above that is missing is the common difference $d$. Note, however, that the common difference can be computed by subtracting the first term to the second term of the sequence. Therefore, if you know the first two terms of an arithmetic sequence, you can find any other term since you already know the value of the first term $a$, and you can easily solve for the value of the common difference $d$. This means that the given statement is true.
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