What is the 68th term of the following sequence and why-
1,4,5,16,17,20...
Sequence problem
- Raiyan Jamil
- Posts:138
- Joined:Fri Mar 29, 2013 3:49 pm
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Re: Sequence problem
The $68$th term of the sequence is $4112$.
The terms of the sequence are either power of $4$ or the sum of the powers of $4$,such as:The first term is $4^{0}$,the 2nd term is $4^{1}$ ,the 3rd term is $4^{0}+4^{1}$ etc.We can get $2^{n+1}-1$ terms by using $o-n$th powers of $4$.So,we can get $2^{6}-1=63$ terms by using $0-5$th powers of $4$.The $63$th term is $4^{0}+4^{1}+4^{2}+4^{3}+4^{4}+4^{5}=1365$.The $64$th term is $4^{6}=4096$.The $65$th term is $4096+1=4097$,the $66$th term is $4096+4=4100$,the $67$th term is $4096+1+4=4101$ and the $68$th term is $4096+16=4112$
The terms of the sequence are either power of $4$ or the sum of the powers of $4$,such as:The first term is $4^{0}$,the 2nd term is $4^{1}$ ,the 3rd term is $4^{0}+4^{1}$ etc.We can get $2^{n+1}-1$ terms by using $o-n$th powers of $4$.So,we can get $2^{6}-1=63$ terms by using $0-5$th powers of $4$.The $63$th term is $4^{0}+4^{1}+4^{2}+4^{3}+4^{4}+4^{5}=1365$.The $64$th term is $4^{6}=4096$.The $65$th term is $4096+1=4097$,the $66$th term is $4096+4=4100$,the $67$th term is $4096+1+4=4101$ and the $68$th term is $4096+16=4112$
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Re: Sequence problem
Convert the terms to base $4$. You'll get the sequence of consecutive binary naturals.
So to find the $n$-th term, convert $n$ to binary, consider the result to be in base $4$ and convert to decimal.
So to find the $n$-th term, convert $n$ to binary, consider the result to be in base $4$ and convert to decimal.
- What is the value of the contour integral around Western Europe?
- Zero.
- Why?
- Because all the poles are in Eastern Europe.
Revive the IMO marathon.
- Zero.
- Why?
- Because all the poles are in Eastern Europe.
Revive the IMO marathon.