How would i write this as a geometric recursive and explicit formula? algebra 2

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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