how are arithmetic and geometric sequences similar
They correspond to linear sequences.
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An arithmetic-geometric mean is a mean of two numbers which is the common limit of a pair of sequences, whose terms are defined by taking the arithmetic and geometric means of the previous pair of terms.
No, but they are examples of linear functions.
The answer depends on the nature of the sequence: there is no single method which will work for sequences which are arithmetic , geometric, exponential, or recursively defined.
Find the 3nd term for 7.13.19
They both are constant and they also have a specific domain of the natural number.
There is no simple answer. There are simple formulae for simple sequences such as arithmetic or geometric progressions; there are less simple solutions arising from Taylor or Maclaurin series. But for the majority of sequences there are no solutions.
A few examples: Counting numbers are an arithmetic sequence. Radioactive decay, (uncontrolled) bacterial growth follow geometric sequences. The Fibonacci sequence is widespread in nature.
Some of them are demographics, to forecast population growth; physicists and engineers, to work with mathematical functions that include geometric sequences; mathematicians; teachers of mathematics, science, and engineering; and farmers and ranchers, to predict crop growth and corresponding revenue growth.
There can be no solution to geometric sequences and series: only to specific questions about them.
Follow this method:
Succession of numbers of which one number is designated as the first, other as the second, another as the third and so on gives rise to what is called a sequence. Sequences have wide applications. In this lesson we shall discuss particular types of sequences called arithmetic sequence, geometric sequence and also find arithmetic mean (A.M), geometric mean (G.M) between two given numbers. We will also establish the relation between A.M and G.M
There are infinitely many arithmetic sequences, and infinitely many geometric sequences, and polynomials, and power equations. Basically, there are too many possible sequences. Arithmetic ones, for example: 13, 14, 15, 16, 17 9, 11, 13, 15, 17 5, 8, 11, 14, 17 1, 5, 9, 13, 17 -3, 2, 7, 12, 17 I hope you get the idea. These are all increasing, and the common differences are integers but both these conditions can be changed.
There aren't any. Geometric is an adjective and you need a noun to go with it before it is possible to consider answering the question. There are geometric sequences, geometric means, geometric theories, geometric shapes. I cannot guess what your question is about.
None. There are relations to power sequences, though.
Nice teaching tool to keep your mind active.
yes a geometic sequence can be multiplication or division
arithmetic sequence * * * * * A recursive formula can produce arithmetic, geometric or other sequences. For example, for n = 1, 2, 3, ...: u0 = 2, un = un-1 + 5 is an arithmetic sequence. u0 = 2, un = un-1 * 5 is a geometric sequence. u0 = 0, un = un-1 + n is the sequence of triangular numbers. u0 = 0, un = un-1 + n(n+1)/2 is the sequence of perfect squares. u0 = 1, u1 = 1, un+1 = un-1 + un is the Fibonacci sequence.
It is an arithmetic sequence. To differentiate arithmetic from geometric sequences, take any three numbers within the sequence. If the middle number is the average of the two on either side then it is an arithmetic sequence. If the middle number squared is the product of the two on either side then it is a geometric sequence. The sequence 0, 1, 1, 2, 3, 5, 8 and so on is the Fibonacci series, which is an arithmetic sequence, where the next number in the series is the sum of the previous two numbers. Thus F(n) = F(n-1) + F(n-2). Note that the Fibonacci sequence always begins with the two numbers 0 and 1, never 1 and 1.
The common difference does not tell you the location of the sequence. For example, 3, 6, 9, 12, ... and 1, 4, 7, 10, .., or 1002, 1005, 1008, 1011, ... all have a common difference of 3 but it should be clear that the three sequences are different. A common difference is applicable to arithmetic sequences, not others such as geometric or exponential sequences.