Integer sequence

  • Thread starter Madonna M.
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  • #1
1. Homework Statement

Provide a simple formula or rule that generates the terms of an integer sequence that begins with :

* 2,4,16,256,65536,....


3. The Attempt at a Solution

I have tried a lot to solve it but i ended up with nothing,although i know that finding a term in the following sequence depends on multiplying the number by itself. For example if i want to get the 3rd term i will multiply the 2nd term by itself (4*4)=16 and same goes to the rest of the sequence,but what about if i want to get the 100th term,of course i won't multiply each term by itself until i reach the needed term,a formula or a rule would be more helpful.

Thanks in advance :)
 

Answers and Replies

  • #2
phinds
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think about what exponents of 2 are needed to give that sequence.
 
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  • #3
could you give me more clear clue please?? :)
 
  • #4
I like Serena
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could you give me more clear clue please?? :)
Your sequence is ##2^1, 2^2, 2^4, 2^8, 2^{16}, ...##.
See the pattern?
 
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  • #5
well,do you mean that every time am going to multiply the power of the previous term by 2 to get the next one?
 
  • #6
Ahaa i got it thanks a lot,i think it would be 2^(2^(n-1))
 
  • #7
I like Serena
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Good! :)
 

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