# Basic Problem

• Oct 26th 2007, 05:23 AM
Pom
Basic Problem
the series 5, 9, 14, 20
what is the equation for the nth term????
• Oct 26th 2007, 10:21 AM
red_dog
$a_1=5$
$a_2=9=5+4=a_1+1+3$
$a_3=14=9+5=a_2+2+3$
$a_4=20=14+6=a_3+3+3$
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So, $a_n=a_{n-1}+(n-1)+3$
$a_n=5+[1+2+3+\ldots+(n-1)]+3(n-1)=5+\frac{n(n-1)}{2}+3(n-1)$