Chapter 12 Sequences and Series - Mixed Review of Problem Solving - Lessons 12.4-12.5 - Page 838: 2b

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From part a, we found the sequence: $1,2^1,2^2,2^3,2^4,2^5$ We can notice that $\frac{a_2}{a_1}=\frac{2}{1}=2\\\frac{a_3}{a_2}=\frac{2^2}{2}=2\\\frac{a_4}{a_3}=\frac{2^3}{2^2}=2\\\frac{a_5}{a_4}=\frac{2^4}{2^3}=2\\\frac{a_6}{a_5}=\frac{2^5}{2^4}=2$ They all give the same ratio $r=2$. Thus, the sequence is geometric.