College Algebra 7th Edition

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

Chapter 8, Sequences and Series - Section 8.3 - Geometric Sequences - 8.3 Exercises: 3

Answer

true

Work Step by Step

RECALL: (1) The $n^{th}$ term $a_n$ of a geometric sequence is given by the formula: $a_n=a\cdot r^{n-1}$ where $a$ = first term $r$ = common ratio (2) The common ratio of a geometric sequence can be found by dividing a term by the term before it. Thus, to find the value of any term, the values of $a$ and $r$ must be known. If the first two terms of a geometric sequence are known, then it means that: (i) $a$ is known; (ii) The common ratio $r$ can be found by dividing the second term by the first term. Thus, knowing the values of the first two terms of a geometric sequence will allow you to find the value of any other term of the sequence. Therefore, the given statement is true.
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