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A Sequence is a list of things (usually numbers) that are in order. Infinite or Finite. When the sequence goes on forever it is called an infinite sequence, otherwise it is a finite sequence. Examples: {1, 2, 3, 4, ...} is a very simple sequence (and it is an infinite sequence) {20, 25, 30, 35, ...} is also an infinite sequence.
A related sequence is the sequence of decimal digits of π, that is, (3, 1, 4, 1, 5, 9, ...). Unlike the preceding sequence, this sequence does not have any pattern that is easily discernible by inspection. Other examples are sequences of functions, whose elements are functions instead of numbers.
What is a sequence? Here are a few lists of numbers: 3, 5, 7 ... 21, 16, 11, 6 ... 1, 2, 4, 8 ... Ordered lists of numbers like these are called sequences. Each number in a sequence is called a term. Sequences usually have patterns that allow us to predict what the next term might be.
- In short, yes. Arithmetic is always adding or subtracting the same constant term or amount. Geometric is always multiplying or dividing by the same...
- NO. Take a look at the difference between the terms of the sequence. The difference between the terms is not constant (not the same), hence not an...
- Yes that is what makes them arithmetic. Multiply and divide are geometric sequences.
- A sequence can be of unreal numbers I think that arithmetic progression should of real numbers
- Simply put if its multiplied or divided it'll be geometric whereas if its added or subtracted its an arithmetic secuence
- Some historical mathematician defined arithmetic sequences has being defined by addition/subtractions of a common value to get from one term to the...
- In this case that is a geometric sequence in which you are multiplying or dividing by a number. An arithmetic sequence would be where you are addin...
- They don't. An *arithmetic sequence* uses addition/subtraction of a common value to create the next term in the sequence. A *geometric sequences* u...
What other sequences are there? Linear and quadratic sequences are particular types of sequence covered their own notes; Other sequences include geometric and Fibonacci sequences, which are looked at in more detail below; Other sequences include cube numbers (cubic sequences) and triangular numbers
Sequences occur naturally in the growth patterns of nautilus shells, pinecones, tree branches, and many other natural structures. We may see the sequence in the leaf or branch arrangement, the number of petals of a flower, or the pattern of the chambers in a nautilus shell.
A sequence is a function whose domain is the counting numbers. A sequence can also be seen as an ordered list of numbers and each number in the list is a term. A sequence may have an infinite number of terms or a finite number of terms. Our sequence has three dots (ellipsis) at the end which indicates the list never ends.
A Sequence is a set of things (usually numbers) that are in order. Each number in the sequence is called a term (or sometimes "element" or "member"), read Sequences and Series for more details. Arithmetic Sequence. In an Arithmetic Sequence the difference between one term and the next is a constant.
