How might interest be described as a problem of sequences?

Question

jamesj · Answer

Ok, what's the formula for a geometric series?
And what's the formula for compound interest?  
How do they compare?

jamesj · Answer

looks pretty similar to me.  What about you?

jamesj · Answer

P     ---> a
1+i ---> r
n    ---> n-1

jamesj · Answer

the principle P grows every time period by (1+i).  This is just like the growth rate in a geometric series of r, where r > 1.

jamesj · Answer

make sense?

jamesj · Answer

In a geometric series, suppose a = 100 and r = 1.1.  Then after one step, a has grown to
ar = 110
One more step and its
121

Now start with $100 and grow it at 10%.  After one time period, the $100 has grown to
$110
One more time period and we're at
$121

etc.

jamesj · Answer

The ratio of the value of the principle one time step later is a constant and that constant is 1+i where i is the interest rate.  This is just like a geometric series where the ratio of successive terms is constant.