The sequence {; }is called the harmonic sequence. True False

Q: If third and seven terms of geometric sequence is 45 and 100 respectively.then find its nineteenth…

A: Given data: The third term is a3=45. The seventh term is a7=100.

Q: What is the closed form for the infinite geometric sequence beginning  4,2,1,1/2 where the first…

A: Given :The infinite geometric sequence : 4, 2, 1, 12, ..

Q: Find an explicit formula for the general term an of the sequence. {1,- -/-/- 3 5

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Q: What is the generating function for the sequence {ck},where ck represents the number of ways to make…

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Q: What is a disadvantage of defining a sequence recursively?

A: The Disadvantage of defining a sequence recursively as In general, recursive functions are slower…

Q: Determine if the sequence is bounded and if it is monotonic. Determine if the sequenc converges and…

A: The given sequence is: an=(-1)nn100 Now, the terms of the sequence are: a1=-1,a2≈1.00,…

Q: Find the 5th term of the geometric sequence with first terma1 = 5 and common ratio r = - 2

A: A geometric sequence is a sequence where each term is found by multiplying the previous term by a…

Q: Provide an Arithmetic Sequence, by either giving a General rule or explicitly listing the first five…

A: We have to provide an Arithmetic Sequence, by either giving a General rule or explicitly listing the…

Q: Show that the sequence 9,12,15,18, ... is an AP. Find its 16th term and the general term.

A: We need to show that the sequence 9, 12, 15, 18, ... is an AP. Here, 12 - 9 = 15 - 12 = 3. And the…

Q: determine whether the sequence with the given nth term is monotonic and whether it is bounded. Use a…

A: Using Desmos graphing calculator, I have got this graph.

Q: PROVE: Reciprocals of a Geometric Sequence If a,, az, az, ... is a geometric sequence with common…

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Q: Explain why 12,6,4,3 is a harmonic sequence. Find its nth term.

A: the given sequence is 12,6,4,3. write the reciprocals of the terms, 112,16,14,13 now note that:…

Q: a,=(- 1)" is a divergent sequence

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Q: What is an example of a sequence that converges to 5?

A: A sequence is convergent to a point "P" , if there is a point "P" which repeats infinitely many…

Q: What's the difference between an arithmetic and g eometric sequence? How do you find the general…

A: What's the difference between an arithmetic and geometric sequence? How to find the general terms of…

Q: What is a monotonic sequence? Under what circumstances does such a sequence have a limit? Give…

A: The monotonic sequence theorem:

Q: Determine the limit of the sequence if it converges. Otherwise, state that the sequence diverges

A: Let an = ln 4nln 3n2

Q: If the 100th term of an arithmetic sequence is 691, and its common difference is 7, then its first…

A: nth term of an arithmetic sequence is given by, an = a1+ (n - 1)d  where a1 is first term and d is…

Q: define: geometric sequence

A: A geometric sequence (or geometric progression) is a sequence, in which each succeeding term of the…

Q: Find x so that x - 1, x, and x + 2 are consecutive terms of ageometric sequence.

A: Given x-1, x, x+2 are the consecutive terms of a geometric sequence. To find x Let t1=x-1t2=xt3=x+2…

Q: What are the first five terms of the sequence defined over the natural numbers with the explicit…

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Q: The generating function of the sequence 4,4,4,4,4 is

A: # To find generating function of sequence  4,4,4,4,4,4 ??

Q: It is a sequence where every term after the first is obtained by multiplying a non-zero constant. O…

A: To tell which is the sequence where every term after the first is obtained by multiplying a non-zero…

Q: A geometric sequence is a sequence in which theof successive terms is constant.

A: In a geometric sequence, the ratio between successive terms is constant. Geometric sequences grow or…

Q: ,(n+), Does the sequences eventually increasing or decreasing ? (2n² – 7n) , (n³ – 4n²), (- , (n +…

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Q: 00 Ink

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Q: Which arithmetic sequence has a first term equal to 47 and a common difference of -18?

A: To find the arithmetic sequence

Q: What is a recursively defined sequence?

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Q: 1,4, 16, 64, ... Identify the type of sequence: How do you know:. Explicit equation: Recursive…

A: The given sequence is 1, 4, 16, 64, ... It is same as 40, 41, 42, 43, ... Now answer the given…

Q: how that the sequence (1 – (-1)" +1/n) is divergen

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Q: Create your own sequence with recursive formula.

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Q: What is a divergent sequence? Give two examples.

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Q: If a sequence is unbounded, then it diverges. True or False?

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Q: A sequence is said to be decreasing sequence if

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Q: If the sequence ~ 9- an - 3 :} converges to 6, then the sequence {an} converges to 9.

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Q: Yes, the sequence is geometric. No, the sequence is not geometric.

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Q: Find the sequence corresponding to generating function 1/(1-az).

A: We will find out the required sequence.

Q: The generating function of the sequence 5,5,5,5,5 is 1-x° (1-x) 1-5x° (1-x) 1- 125x (1-x) 1-3125x…

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Q: {an} = {2(-1)"+1}

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Q: Show that the sequence {1, -1, 1, -1, 1, -1, ..., (-1)n+1, ...} diverges.

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Q: The generating function for the sequence 1,0,1,0,1,0,1 is

A: We have to find the generating function for the sequence  1 , 0 , 1 , 0 , 1 , 0 ,1  = 1 + 0(x) +…

Q: Find an explicit formula for the sequence 1/2,-1/3,1/4,-1/6....

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Q: Discuss the non decreasing and Bounded of the sequence 5,5,5,5,5

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Q: 1. Find the 30th term of the 1 1 1 harmonic sequence ,0, –? - - - 4'2' 2 2 How many multinles of -

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

Q: What is the 11th term of the geometric sequence −1.5,−3,−6,−12,…?

A: Given series ,-1.5 , -3 , -6 , -12 ,---first term , a1=-1.5Common ratio , r=-3-1.5=2

Q: The twentieth term of sequence an = %3D 11+1

A: Here is the solution:

Q: Show that if a and x are any two nonzero real numbers, then ,-1,,-.. is a geometric sequence.

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Q: If the sequence { 2-4 an an+2 } converges to 7, then the sequence {an} converges to 9. True or…

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