## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 5 - Number Theory and the Real Number System - 5.7 Arithmetic and Geometric Sequences - Exercise Set 5.7: 101

#### Answer

(i) The sequence is geometric. (ii) The next two terms are: 405 and 1,215.

#### Work Step by Step

A sequence is: (a) arithmetic if there is a common difference among the terms. (b) geometric if there is a common ratio among the terms. Notice that in the given sequence, the next term is three times larger than the previous term. This means that the sequence has a common ratio of 3. Thus, the sequence is $\underline{\text{geometric}}$. The next two terms can be found by multiplying 3 to the previous term. Therefore, the next two terms are: $135(3) = 405 \\405(3)=1215$

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