## Precalculus: Mathematics for Calculus, 7th Edition

$a_{n}=\displaystyle \frac{n+2}{n+3}$
For $a_{1}$, the numerator=1+2, the denominator = 1+3 For $a_{2}$, the numerator=2+2, the denominator = 2+3 For $a_{3}$, the numerator=3+2, the denominator = 3+3 For $a_{4}$, the numerator=4+2, the denominator = 4+3 The subscripted index of the term is increased by 2 to obtain the numerator, and increased by 3 to obtain the denominator of the term., The pattern leads to the general term: $a_{n}=\displaystyle \frac{n+2}{n+3}$