Integer Sequence: Solve & Generate Terms

[Madonna M.]

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 :)

 

[phinds]

think about what exponents of 2 are needed to give that sequence.

 

[Madonna M.]

could you give me more clear clue please?? :)

 

[I like Serena]

could you give me more clear clue please?? :)

Your sequence is $2^1, 2^2, 2^4, 2^8, 2^{16}, ...$.
See the pattern?

 

[Madonna M.]

well,do you mean that every time am going to multiply the power of the previous term by 2 to get the next one?

 

[Madonna M.]

Ahaa i got it thanks a lot,i think it would be 2^(2^(n-1))

 

[I like Serena]

Good! :)