Let an be the n" element of the sequence 6,12,24,48, ... then an=ar" for constant values r and a. What is r?

Q: The sum of the first n terms of a sequence is given by S, = 3" +1 - 6 3.1. Determine the sum of the…

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Q: Is the sequence {cos (-)- In(n)}, monotone? If so is it increasing creasing? or de-

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Q: Find the first five terms of the given recursively defined sequence. a,= 2(a,1 – 2) and a, = 3 %3D n…

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Q: Let Fn be Fibonacci sequence. Prove that:

A: By the definition of the Fibonacci sequence, Fn+2=Fn+1+Fn and the Fibonacci sequence is satisfied…

Q: The following infinite sequence will be defined as recurrent relation: 1,10,3,20,9,30,27,40, ... The…

A: This question is related to sequences. The solution to the given question is explained below.

Q: a. 2, 8, 26, 80, 242 b. 1, 2, 3, 4, 5 c. 1, 3, 9, 27, 81 d. -1, 2, 8, 26, 80

A: First five terms of the sequence defined over the natural numberswith the explicit function…

Q: .A sequence can be generated by using an = a(n-1) + 6, where a = 3 and n is a whole number greater…

A: The given sequence is an=an-1+6 where a1=3. Put n = 2,  a2=a1+6=3+6=9 Put n = 3, a3=a2+6=9+6=15 Put…

Q: If do, a1, a2, A3, ... is a sequence of increasing real numbers, then for large enough j it is the…

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Q: Suppose that ho, hị, h2, . is a sequence defined as follows: ho = 1, h1 = 2, h2 = 3, %3D hy =…

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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: the Sequence hver So Lalue. for

A: The given sequence is,

Q: The first four terms of the sequence defined by an = nan-1+n°n_2,40=1, a1 = 5 are %3D a0 = 1, a1 =…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: The Fibonacci number is a sequence which is described explicitly by Fn = Fn-1 + Fn-2-

A: Given statement is The Fibonacci number is a sequence which is described explicitly by  Fn = Fn-1 +…

Q: A sequence ao, a1, a2, .. .satisfies an = n an-1+(-1)" for n > 1. If a5 = 44, then az %3D

A: Since, a sequence a0,a1,a2,..... satisfies an=n.an-1+(-1)n-(i) for n≥1.Ifa5=44. Our Aim is to find…

Q: A sequence of numbers a1, a2, a3, ... is defined by = 3 ап+1 An -2 -3 пEN An 100 Find ar r=1

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Q: Find the 70th term of the following arithmeti c sequence. 4, 11, 18, 25

A: First term of the A.P. is 4 Common difference, means the difference between two consecutive terms is…

Q: 4. Write down the first six terms of the Fibonacci =1 and F2 = 1. sequence defined by Fn Fn-1 +…

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Q: Suppose that a sequence is defined a=-3, + 10 n-1 List the first four tor mc of th

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Q: Consider the sequence: 17, 14, 11, 8, ..., find the 26th term of the sequence.

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Q: Select all sequences that will contain infinitely many square numbers. А. а, — п В. а, — 4n + 1 C.…

A: We have to check which of the given sequence contains infinitely many square numbers. (A) Given an=n…

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

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Q: Suppose that the sequence {ax}ı is k= 1,3, 5, 7, 9, 11, 13,.. What is a;?

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Q: This is sequence and the is equal to

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Q: Suppose ao, a1, a2,... is a sequence such that ao = a1 = 1 and forn2 1, an+1 = n(an+an-1). Find az =…

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Q: The fourth term of an arithmetic sequence is 10 and the 20Oth term is 58. Determine the first four…

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Q: , n=1,2,3. is a sequence of real numbers defined by a, = /2 %3D %3D and for n21, a = 2,/2+a, .

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Q: 2. Suppose x,, X2 , X3 ..... Isa sequence defined by x, = 2, X2 = 4, bk-2 + 2bk-1 for all integers k…

A: Since you have asked multiple questions, we will solve the first question for you. Note:- In…

Q: a sequence having {2,3,5,11,13} as lts set öf points.

A: Explanation of the answer is as follows

Q: Consider the following sequence: 3,9,15,21,... Find the 50th term of this sequence.

A: This is an arithmetic sequence with the common difference =d= 9-3=6 And the first term = a_1= 3

Q: Use the pigeonhole principle to show that there is a multiple of 691 whose digits are Os and 1s.…

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Q: The first four terms of the sequence defined by An = nan-1+n'an-2, ao = 3, aj= 5 are ao = 3, a1 = 5,…

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Q: The five first terms of the sequence {4n–1}=1 are: O 3,7,11,15,19,... O 3+7+11+15+ 19... O…

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

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Q: Let an be the nh element of the sequence 5,8,11.14,17,., then an.dxn+c for constant values d and c.…

A: What is d??

Q: Suppose that the sequence {az}ı is k=1 1,3, 5, 7,9, 11, 13,.. What is a1?

A: First we find the general of the given sequence {ak}∞k=1=1,3,5,7,9,11,13,..., with the help of…

Q: A sequence a1, a2, a3,.... satisfies the property that an+1 is the average of the first n terms if…

A: We have to find a2 .

Q: 4. Let (bn) be a sequence defined by 4bn-2 - bn-1 n > 2 b, n = 1 -1 n = 0

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Q: The first four terms of the sequence defined by an = nan 1+n'a, 2, ao = 2, a1 = 6 are %3D O ao = 2,…

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Q: 35. Prove that the sequence {n!}^, beats the sequence {2"}-1-

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Q: If the sequence {a,} is defined as follows: Ha,=1, a,+1= 15-a, for n > 1 then as %3D %3D

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Q: A sequence a1, a2, a3,….. is defined by An+1 4аn — 3, п > 1 -- = k, where k is a positive integer.…

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

A: Here is the solution:

Q: B. Express a, in terms of n for each of the following sequences. 4. 2, 4, 8, 16,... 5. 5, 11, 21,…

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Q: Determine the explicit formula for the following sequences. 2. Sequence: 6, -6, 6, –6, 6, ... a, = 6…

A: Solution is given below:

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

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Q: Show that the real sequence ( 0,-1,2,-3 , .... , (-1)nn, .... ) where n is a value from the set of…

A: Consider the given sequence,

Q: Let ao, a1, a2, . .. be a sequence defined recursively by ak-1 + 6ak-2, ak for each integer k > 2…

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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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Q: Let 3, 10, 17, 24, 31,......be a sequence. Find an expression for its nth term i.e an and find a36

A: The given sequence is 3, 10, 17, 24, 31… Let assume that n > 0 for the sequence.