SOLUTION: A sequence {m<sub>n</sub>} is recursively defined as m<sub>1</sub>=2, m<sub>n+1</sub>=3/5-m<sub>n</sub>

Algebra ->  Sequences-and-series -> SOLUTION: A sequence {m<sub>n</sub>} is recursively defined as m<sub>1</sub>=2, m<sub>n+1</sub>=3/5-m<sub>n</sub>      Log On


   

Question 1017792: A sequence {mn} is recursively defined as
m1=2, mn+1=3/5-mn
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
A sequence {mn} is recursively defined as
m1=2, mn+1=3/5-mn

substitute n=1
m1+1=3/5-m1
m2=3/5-2 = 3/5-10/5 = -7/5

substitute n=2
m2+1=3/5-m2
m3=3/5-(-7/5) = 3/5+7/5 = 10/5 = 2

Wow! We're right back where we started.  If we continue
with this recursion formula:

substitute n=3
m3+1=3/5-m3
m4=3/5-2 = 3/5-10/5 = -7/5

substitute n=4
m4+1=3/5-m4
m5=3/5-(-7/5) = 3/5+7/5 = 10/5 = 2

So the sequence goes:

2, -7/5, 2, -7,5, 2, -7/5, ...

Edwin