Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.3 Geometric Sequences; Geometric Series - 12.3 Assess Your Understanding - Page 825: 75

Answer

Neither arithmetic nor geometric

Work Step by Step

We are given the sequence: $1,3,6,10,......$ Compute the difference between two consecutive terms: $3-1=2$ $6-3=3$ $10-6=4$ As the difference between any consecutive terms is not constant, the sequence is not arithmetic. Compute the ratio between two consecutive terms: $\dfrac{3}{1}=3$ $\dfrac{6}{3}=2$ $\dfrac{10}{6}=\dfrac{5}{3}$ As the ratio between any consecutive terms is not constant, the sequence is not geometric. So the sequence is neither arithmetic nor geometric.
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