How would I write this as a geometric recursive and explicit formula? Algebra 2
1 answer:
Denote the sequence by
with
.
Recursively:
The first number is
, and each successive number is twice the previous one. So
,
,
, ... .
In other words,
and so in general,
Explicitly:
We can arrive at this formula by, in a way, working backwards. If
, that means
, and so
, and so on. We would end up with
(You'll notice a pattern here: the exponent of the 2 and the index of the earlier term in the sequence add up to
. For example,
.)
or simply
Then the 15th term is obtained immediately by evaluating this rule at
. We get
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