Find an explicit formula for the following sequences with the initial given terms a , a , a , . 2 3 a) (1 - (-), (2;); (- ;-); (“ ;2) 3 6 h 42 16 _25 9 27 3 81 243

Q: Suppose that the sequence {ak}1 is 2, 4, 6, 8, 10, 12, 14, 16, . What is a,?

A: we have the given sequence 2,4,6,8,10,12,14,16,...

Q: 4n2 + 2n + 6 6, 15, 24, ...,

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Q: 2. Find the closed form for the generation function for the sequences (i) 2, -2, 2, -2, 2, -2, - - -…

A: The closed form for the generation function for a sequence is used to define the general term of a…

Q: Let {n} be a sequence. Let Yn = if {n} is monotonic, 1. Show that n then so is {yn}.

A: What is Monotone Sequence: A sequence can either be constant or monotone. There are two different…

Q: Find the first five terms of these recursively-defined sequences: 9. a1 = 2, an = 2an-1 - 5

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find the 9th term for the sequence of positive 3 digit numbers that are multiples of 5.

A: We have to find the 9th term for the sequence of positive 3 digit numbers that are multiples of 5…

Q: The Sum of Terms of a Sequence Suppose that a virus enters a community and the number of new…

A: We need to describe mathematical difference.

Q: Find the sequences of difference for those sequences given below. For example, for the sequence an:…

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Q: Which sequence could be described by the first term: Aj = 1 and the recursive (an)² + 1 definition:…

A: Given, an+1=an2+1 a1=1

Q: help please

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Q: 1 and the recursive Which sequence could be described by the first term: aj 2 definition: An+1 =…

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Q: 1. For each of the following sequences, write down the first 4 terms of the sequence (an). (a) (급),…

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Q: Click on all of the sequences that are arithmetic (There is more than 1 ans 8, 13, 18, 23, 28

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Q: In your own language, describe the pattern of the following sequences (The sequences are given as a…

A: We draw required connection between the pattern and formulas as below.

Q: What is the sequence function (an) for the following 1 2, 1.2, 3 3

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Q: Give the first six terms of the following sequences. You can assume that the start with an index of…

A: Increasing sequence : If an is any sequence and an≤an+1 for all n .Then an is called to be…

Q: What are the first 5 terms (starting with ao) of the sequence described below? an = 2an-1 - an-2…

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Q: Match each of the following sequence statements with the correct sequence. a, =3a a +3 for n2 1 and…

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Q: Find the recursive formula of the following sequence. (4, 7, 15, 24, . ... a1 = 4, a, = an-1+ 3(n +…

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Q: Write an explicit formula and a recursive formula for the following sequence: 32, 26, 20, 14, 8,.…

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.