anemone said:The increasing sequence 1, 3, 4, 9, 10, 12, 13 ... consists of all those positive integers which are powers of 3 or sum of distinct powers of 3. Find the 100th term of this sequence.
caffeinemachine said:Let $n=(a_ka_{k-1}\ldots a_1a_0)_2$. Then the $n$-th number in the sequence is $3^ka_k+3^{k-1}a_{k-1}\cdots+3^1a_1+a_0$. It hinges on the fact that $3^{r+1}>1+3+\cdots+3^r$. Therefore the 100th number is $3^6+3^5+3^2$.
Keep such problems coming anemone!anemone said:Hi caffeinemachine, thanks for participating in the problem and your answer is correct.:)
I want also to say that at MHB, we are never short of talented maths experts here, and I've gained some very useful insights from the site, and for this I am so thankful!;)
caffeinemachine said:Keep such problems coming anemone!
Not really.. In the olympiad genre I am an 'ardent fan' of Combinatorics and Geometry questions. In curriculum mathematics I like Discrete math the most, esp Algebra and Combinatorics. And among the mathematical disciplines in which I am a newbie I find Relativity and Non Euclidean Geometry the most fascinating and Romantic.anemone said:Hey caffeinemachine, are you one of the ardent fans of sequences and series? (Nerd)
How about you? Your math interests?anemone said:Hey caffeinemachine, are you one of the ardent fans of sequences and series? (Nerd)
caffeinemachine said:Not really.. In the olympiad genre I am an 'ardent fan' of Combinatorics and Geometry questions. In curriculum mathematics I like Discrete math the most, esp Algebra and Combinatorics. And among the mathematical disciplines in which I am a newbie I find Relativity and Non Euclidean Geometry the most fascinating and Romantic.
- - - Updated - - -How about you? Your math interests?
A sequence is a list of numbers that follow a specific pattern or rule. Each number in the sequence is called a term.
To find the 100th term of a given sequence, you need to know the pattern or rule that the sequence follows. Then, you can either use a formula or manually calculate each term until you reach the 100th term.
Yes, there can be multiple ways to find the 100th term of a given sequence depending on the pattern or rule that the sequence follows. Some sequences may have a simple formula, while others may require more complex calculations.
Yes, it is crucial to know the pattern or rule of a sequence in order to find the 100th term accurately. Without understanding the pattern, you may end up with an incorrect answer.
Yes, you can use a computer program to find the 100th term of a given sequence. There are various mathematical software and programming languages that can help with this task, making it faster and more efficient.