## Algebra 2 Common Core

Published by Prentice Hall

# Chapter 9 - Sequences and Series - 9-1 Mathematical Patterns - Practice and Problem-Solving Exercises - Page 569: 22

#### Answer

$a_{n}=na_{n-1}$

#### Work Step by Step

Sequence starts with 1 so $a^{1}=1$ Then $a_{2}=2*1$ $a_{3}=3*2=3*a_{2}$ $a_{4}=4*6=4*a_{3}$ $a_{5}=5*24=5*a_{4}$ Notice that the first factor in the factored form of the term;s value is the same as the term number, while the second factor is the same as the value of the previous term. Thus, letting $n$ be the term number, the recursive formula for the sequence is: $a_{n}=na_{n-1}$

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