## Algebra 2 (1st Edition)

Published by McDougal Littell

# Chapter 12 Sequences and Series - Investigating Algebra Activity - 12.5 Exploring Recursive Rules - Draw Conclusions - Page 826: 3

#### Answer

$\left\{\begin{array}{l} a_{1}=81,\\ a_{n}=a_{n-1}/3 \end{array}\right.$

#### Work Step by Step

We note that all the given terms are powers of 3: $81\div 3=27\qquad\rightarrow\qquad a_{2}=a_{1}/3$ $27\div 3=9\qquad\rightarrow\qquad a_{3}=a_{2}/3$ $9\div 3=3\qquad\rightarrow\qquad a_{4}=a_{3}/3$ $3\div 3=1\qquad\rightarrow\qquad a_{5}=a_{4}/3$ $1\div 3=1/3\qquad\rightarrow\qquad a_{6}=a_{5}/3$ $...$ A general rule:$\qquad a_{n}=a_{n-1}/3$ A recursive rule for the sequence: $\left\{\begin{array}{l} a_{1}=81,\\ a_{n}=a_{n-1}/3 \end{array}\right.$

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