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Integer sequence

  1. Oct 5, 2013 #1
    1. The problem statement, all variables and given/known data

    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 :)
     
  2. jcsd
  3. Oct 5, 2013 #2

    phinds

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    think about what exponents of 2 are needed to give that sequence.
     
  4. Oct 5, 2013 #3
    could you give me more clear clue please?? :)
     
  5. Oct 5, 2013 #4

    I like Serena

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    Your sequence is ##2^1, 2^2, 2^4, 2^8, 2^{16}, ...##.
    See the pattern?
     
  6. Oct 5, 2013 #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?
     
  7. Oct 5, 2013 #6
    Ahaa i got it thanks a lot,i think it would be 2^(2^(n-1))
     
  8. Oct 5, 2013 #7

    I like Serena

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    Good! :)
     
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