"The action sequences are absolutely breathtaking."
"First term, common difference, formula - all set!"
"Quick math trick: flipping sequences for AP ease!"
"In an arithmetic sequence, the pattern is based on addition and subtraction. In a geometric sequence, the pattern is based on multiplication and division."
"You want to come up with different sequences that you string together to tell your story."
"So the cool part about this is that because this is our... this has to be an element of the sequence anyway, because there's no other way to have the gcd be this, you can use this to separate the values."
"Nothing will be cooler than these opening credit sequences."
"You can use them in your sequences and projects to get great-looking results."
"This movie contains some of the best sequences I've seen in film this year."
"Arithmetic progressions are some of those kind of basic sequences you'd find on GCSE."
"It's all just encased inside this house, all of the murders, all of the deaths, all of the scary sequences."
"Considerable challenges came when shooting the film's most incredible sequences."
"They must necessarily contain arithmetic progressions."
"...there are some really funny things that happen and there are some really ingenious sequences."
"I really love how that all plays out and it leads to a lot of amazing sequences."
"Some of these sequences are legitimately intense, like this one part where they attempt to raft back to the mainland on a log, only for a Kratosaur to appear."
"I wouldn't describe any of these sequences being majorly game-changing."
"This whole fight has a lot of really cool long sequences."
"What's important in any of these sequences is that you tune your control loops."
"You can have many different sequences and you can also make a whole beat under one sequence."
"I thought the sequences with the food just, you can't watch this on an empty stomach."
"A brief series of wordless panels can be a great way of conveying a sense of location prior to a scene getting underway."
"If a n comes from the interval from 1 to 2 then a n plus 1 is also in the interval from one to two."
"What you're seeing here is actually a sequence of canonical representations."
"We subdivide the image sequence into sub-sequences."
"He was brilliant in the action sequences."
"This is a product of three consecutive numbers."
"That sequence there has an nth term n plus 13."
"So N squared plus n plus 13 would be your nth term of this quadratic sequence here."
"If this comes out as a constant difference down here, that's great, you can just put that after the N squared part."
"That's what X1 is, 5 divided by the current number squared."
"The pattern here is previous number plus the sequence number multiplied by two."
"We say that this sequence \( c_n \) converges to \( c \) if for all \( \epsilon \) bigger than zero, there is an \( N \) such that if \( n \) is bigger than or equal to this capital \( N \), the modulus of \( c_n - c \) is less than \( \epsilon \)."
"A sequence of real numbers is said to be bounded if there is a real number \( M \) such that the absolute value of \( a_n \) is less than \( M \) for all natural numbers \( n \)."
"For each... calls the function for every element in the sequence."
"When you have a set of numbers where the order matters, it's called a sequence."
"Sequences can be finite or they can be infinite."
"We have a concept called sequences in Snowflake... create sequence sequence one."
"Yes, 126 is a term in this sequence and it's the 11th term."
"What's really interesting about this is not the series itself but the ratios that are inside those numbers."
"Transformers can model much longer sequences well."
"Triangular numbers are the numbers that can be represented as a sum of consecutive integers starting with one."
"Beyond that, there's some great action sequences."
"Every bounded monotonic sequence converges."
"If I wanted to get the 100th row of this table, I would have to generate all the rows in between, but eventually, I could get down to row number 100 just by addition."
"A geometric sequence is a sequence of numbers where you go from one number to the next number by multiplying by the same amount each time."
"An exponential relationship is like a geometric sequence."
"The nth term of a sequence is equal to the first term plus \( (n-1) \) times the common difference."
"John Wick 4 has some of the best action sequences I've ever seen."
"An arithmetic sequence can always be written as \( a_n = a_1 + (n - 1) \times d \)."
"If you can identify that something is a specific type of sequence or series, it becomes a lot more predictable."
"We have X over 1 minus x minus x squared raised to the M plus one, and that's a nice final version for this generating function for the M convolved Fibonacci sequence."
"A probability tree diagram shows probabilities for sequences of two or more events."
"To find the probability of a sequence of events, you multiply along the branches representing those events."
"The idea to make a sequence the coefficients of a power series is pretty simple and yet it yields a tremendously powerful combinatorial technique."
"The geometric sequence is something that you learn usually in algebra, but it doesn't come into its own as something really useful to know about until a little bit later in math."
"Now the good news is, geometric sequence is very simple to understand."
"Geometric sequences have a common ratio; they increase or decrease through multiplication."
"Recurrent neural networks are very useful for representing temporal sequences as in speech or sequences of words in a sentence."
"Let me show you what I mean by time series and sequences because there's some important concepts for the code that we're going to actually create."
"A geometric progression is where you've got a common ratio between each term of the sequence."
"The Fibonacci sequence is where each term is the sum of the two previous ones."
"We want to start reasoning about sequences of random variables that keep going on, in principle, forever."
"There are two really important types of sequences: arithmetic and geometric."
"The coefficient on the n is half of the second difference."
"The colon operator produces a row vector of evenly spaced numbers."
"Factorials... you're taking the number and multiplying it by every number that comes before it."
"I observable of T represents one thing after another."
"Essentially arbitrary sequences can be represented either as linear combinations of complex exponentials, or as linear combinations of sinusoidal sequences."
"If you have a bunch of points of a sequence, they converge to some point \( P \) if no matter what epsilon you give me, there is some point in the sequence beyond which all the points are within epsilon of \( P \)."
"The solutions are getting closer and closer to the roots, therefore this is what we call a convergence sequence."
"The geometric sequence has great importance in mathematics."
"The sequence is actually a two-level sequence. There is a sequence of adding nodes, and there is a sequence of adding edges."
"There are two to the power n n-bit sequences."
"A sequence converges if no matter what distance you name from the proposed limit, there's a point of the sequence beyond which all the terms are close to the limit."
"...why do we want to generate sequences in the first place? This kind of speaks to generative models in general..."
"A sequence is Cauchy if for every epsilon greater than zero, the terms of the sequence eventually are all within epsilon of each other."
"All recursive equations mean is you're going to use the previous one to find the next one."
"Causality ensures the existence of a convergent subsequence."
"Let's first generate a list from one to n and then take the product of that list."
"A sequence converges to some number L if for every epsilon greater than zero there is some natural number big N such that whenever little n is greater than that big N the distance between a sub little N and L is less than Epsilon."
"Let's jump right into it and start to see how we can add up the terms of a geometric sequence to create a geometric series."
"Geometric sequences with common ratios greater than one grow very quickly."
"We can generate these famous sequences by using a recurrence relation."