How do you write a rule for the nth term of the geometric sequence, then find a6 given 2, 14, 98, 686,...?
Geometric sequences are defined by the simple formula:
or some variation of it. Our task, most of the time is to find
In this case, if you start dividing each of the known members by the previous one (eg.
Looking from the begining (let's start at n=2) we have that:
Notice that the last part of each line is
This allows us to write:
as the final formula for any number in the sequence.
Now I can open my calculator and find that