The sequence (a[n]) satisfies a[1] = 3 and
a[n] = (a[n-1] − 1) / (a[n-1] + 1)
for all n ≥ 2. Find a[100].
Anything in '[]' is meant to signify a subscript. Thanks in advance.
Let's see if we can find a pattern
The terms are
3 , 2/4 , -1/3 , -2 , 3
Note that the period will repeat after every 4 terms
So 100/4 = 25 complete periods
So a100 = -2
+69 
