Calculus
# Sequences and Series

$\frac11, \frac21, \frac12, \frac31, \frac22, \frac13, \frac41, \frac32, \frac23, \frac14, \cdots$

If the $n^\text{th}$ term of the above sequence is $\frac{3}{15}$, what is $n$?

A sequence $\{a_n\}$ with $a_n>0$ for all $n(\ge 1)$ satisfies

$\frac{a_{n+1} - a_n}{a_{n+1} + a_n} = \frac12.$

If $a_1 = 2$, what is $a_5$?