Recall that every geometric sequence has a common ratio
r. Therefore, it is possible to find every term of the sequence by multiplying the first term
a1 by this common ratio a particular number of times. Therefore, knowing
a1 and
r is enough to describe the whole geometric sequence.
It is easier to identify a that can be used to write a general for the explicit rule by making a . Note that by the ,
r0 is equal to
1. Furthermore,
r can be written as
r1.
n |
an |
Using a1 and r
|
1 |
a1 |
a1⋅r0
|
2 |
a2 |
a1⋅r1
|
3 |
a3 |
a1⋅r2
|
4 |
a4 |
a1⋅r3
|
It can be seen that the of the common ratio is always 1 less than the value of the position n. With this pattern, it is possible to write the explicit rule in the same form as the given at the beginning.