Chapter 12 Sequences and Series - 12.1 Define and Use Sequences and Series - Guided Practice for Examples 2 and 3 - Page 795: 4

$a_{n}=(n+1)^{2}-1$ $a_{5}=35$ Graph: .

We may recognize a pattern such as $n=1,\quad a_{1}=3=4-1=2^{2}-1$ $n=2,\quad a_{2}=8=9-1=3^{2}-1$ $n=3,\quad a_{3}=15=16-1=4^{2}-1$ $n=4,\quad a_{4}=24=25-1=5^{2}-1$ The pattern that emerges is that $a_{n}=(n+1)^{2}-1$ The next term would be $a_{5}=6^{2}-1=35$ To graph, plot the points (1,3), (2,8), (3,15), (4,25) (5,35).