## 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: 4

#### Answer

For an arithmetic sequence, $a_{n}=a_{n-1}+d.$ For a geometric sequence, $a_{n}=r\cdot a_{n-1}.$

#### Work Step by Step

For an arithmetic sequence, the terms $a_{n}$ and $a_{n-1}$ are such that $a_{n}-a_{n-1}=d,\qquad$ ... They share a common difference between consecutive terms ... Adding $a_{n-1}$ to the equation, we obtain $a_{n}=a_{n-1}+d$ For a geometric sequence, the terms $a_{n}$ and $a_{n-1}$ are such that $\displaystyle \frac{a_{n}}{a_{n-1}}=r,\qquad$ ... They share a common ratio between consecutive terms ... Multiplying the equation with $a_{n-1}$, we obtain $a_{n}=r\cdot a_{n-1}$

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