SOLUTION: Given the sequence 1,4,16,64 write an explicit formula for the nth term of the sequence in f(n) notation

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Question 1026054: Given the sequence 1,4,16,64 write an explicit formula for the nth term of the sequence in f(n) notation
Found 2 solutions by ikleyn, jim_thompson5910:
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
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Given the sequence 1,4,16,64 write an explicit formula for the nth term of the sequence in f(n) notation
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Geometric progression with the first term a = a%5B1%5D = 1 and the common ratio r = 4.

The formula for the general term is a%5Bn%5D = a%5B1%5D%2Ar%5E%28n-1%29 = 4%5E%28n-1%29, n = 1, 2, 3, 4, . . . 

See the lesson Geometric progressions in this site.


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
This is a sequence of terms that are powers of 4

1 = 4^0
4 = 4^1
16 = 4^2
64 = 4^3
and so on...

So the nth term is 4%5E%28n-1%29 where n is an integer and it starts at n = 1.

So the function is f%28n%29+=+4%5E%28n-1%29 and we make the restriction on the domain that n is an integer and n+%3E=+1 or n+%3E+0