Geometric sequence essay

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November 30, in puzzles , Real life maths Tags: geometric series , zeno Leave a comment. This is a very famous paradox from the Greek philosopher Zeno — who argued that a runner Achilles who constantly halved the distance between himself and a tortoise would never actually catch the tortoise. The video above explains the concept. There are two slightly different versions to this paradox. The first version has the tortoise as stationary, and Achilles as constantly halving the distance, but never reaching the tortoise technically this is called the dichotomy paradox. The second version is where Achilles always manages to run to the point where the tortoise was previously, but by the time he reaches that point the tortoise has moved a little bit further away.

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Sequences: Arithmetic and Geometric

For example, the following is a geometric sequence,. From this we see that any geometric sequence can be written in terms of its first element, its common ratio, and the index as follows:. The terms between given terms of a geometric sequence are called geometric means In this case, we are given the first and fourth terms:. A geometric series 22 is the sum of the terms of a geometric sequence. However, the task of adding a large number of terms is not.

Arithmetic and Geometric Sequences

We use cookies to give you the best experience possible. Words: , Paragraphs: 4, Pages: 2. Paper type: Essay , Subject: Geometry. A sequence is a set of real numbers. It is a function, which is defined for the positive integers.
The sequence is described as a systematic collection of numbers or events called as terms, which are arranged in a definite order. Arithmetic and Geometric sequences are the two types of sequences that follow a pattern, describing how things follow each other. When there is a constant difference between consecutive terms, the sequence is said to be an arithmetic sequence ,. On the other hand, if the consecutive terms are in a constant ratio, the sequence is geometric. In an arithmetic sequence, the terms can be obtained by adding or subtracting a constant to the preceding term, wherein in case of geometric progression each term is obtained by multiplying or dividing a constant to the preceding term.
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