Which sequences are arithmetic12/23/2023 ![]() Sequence is any group of numbers with some pattern. All exercise questions, examples, miscellaneous are done step by step with detailed explanation for your understanding. Solutions of Chapter 8 Sequences and Series of Class 11 NCERT book available free. Hopefully, by studying the graphs of different sequences, students willobtain a better understanding of sequences and how they are related to otherfunctions.Updated for new NCERT - 2023-2024 Edition. Will all geometricsequences be exponential? How are these sequences related to other functions? But unlike the previous ones, these graphs are decreasing exponentially whereas, the previous ones were increasing exponentially. The graphs of these sequences have a similar shape to the previous ones. Look at the following spreadsheet.Īre the graphs of these geometric sequences similar to the graphs ofthe above geometric sequences? Let's graph them to see. In this example, we are investigatingthe sequence of (1/3)^n and variations on it. A geometric sequence goes from one term to the next by always multiplying (or dividing) by the same value. Now, graph these sequences to determine their shape.įrom observing the above graphs, the shape of these geometric sequencesare exponential. The following geometric sequences are 2^n and variations on this sequence. What can you conclude about arithmetic sequences? Are they all linear? How are these sequences related to other functions? The purple line is the graph of 1/2n-4/5. Practice identifying both of these sequences by watching this tutorial Keywords: sequence arithmetic sequence geometric sequence common ratio common. Examine the followingspreadsheet.įrom examining the spreadsheet and from our knowledge of functions andgraphs, these sequences appear to have linear graphs also. We are going to examinethe sequence 1/2n and variations of this sequence. The green line is the graph of 4n-2 and the red line is thegraph of 4n-19.ĭo all arithmetic sequences have linear graphs? Let's examine anotherarithmetic sequence to see if its graph is linear. ![]() If we look at the graphs of these sequences, we notice that they areall linear. is arithmetic because the difference between consecutive terms is always two. The following is an example of the arithmetic sequence 4n and variationsof this sequence. In an arithmetic sequence, the difference between consecutive terms is always the same. A geometricsequence is a sequence in which each term after the first term is obtainedby multiplying the preceding term by a constant nonzero real number, calledthe common ratio. ![]() An arithmetic sequenceis a sequence in which each term after the first term is obtained by addinga fixed number, the common difference, to the previous term. A finite sequence is whenthe domain is the set and an infinite sequence is a sequencewhose domain is the set of all natural numbers. There aretwo kinds of sequences, finite and infinite. All the elements of a sequence are ordered. A geometric sequence (sometimes called geometric progression) is a sequence of numbers in which the ratio r between consecutive terms is always constant. (each number is 3 larger than the number before it) See: Sequence. An arithmetic sequence is a type of sequence in which the difference between each consecutive term in the sequence is constant. ![]() A sequence is definedas a function, an, having a domain the set of natural numbers and the elementsthat are in the range of the sequence are called the terms, a1, a2, a3.,of the sequence. A sequence made by adding the same value each time. This essay is designed to help studentsdevelop a better understanding of these sequences by investigating and interpretingvarious kinds of graphs.īefore I begin my investigations of sequences, I want to give a few definitionsso that we will all be starting from the same point. Students are introduced to various arithmetic andgeometric sequences in high school. In this essay, I am going to investigate different arithmetic and geometricsequences using Excel. ![]()
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