The generating function of the sequence 3,3,3,3,3 is 1-x5 (1-x) 1-3x° O 11-x) 1-27x (1-x) 1-243x (1-x)

Q: Fin the 9th term in the harmonic sequence 1/11, 1/15, 1/19, 1/23, ..? What is the nth term of the…

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Q: The first 2 terms of the Fb sequence are: 1, and 1. Find the 14th and 16th terms of the Fb sequence.

A: The first 2 terms of the Fb sequence are: 1, and 1. So we can write the rule: The Rule is xn = xn−1…

Q: Find the generating function for the sequence: 1-5,5,5,5 2-1,5,25,125,…………. 3-6,6,6,000,…

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Q: Find the first four terms and the eighth term of the sequence.

A: Consider a sequence an. Then, the terms of the sequence are given by: a1, a2, a3..., an, .... where…

Q: 2. Find and prove a closed formula for the recursive sequence a, = 3, a, =a-2 %3D

A: Topic = Sequence

Q: Find the first five terms and the 14" term of a sequence with 2n +1 general term a, 2n-1

A: Given,         The first five terms and the 14th term of a sequence with the general          term ,…

Q: Give the first three terms of each sequence based on the given a1=4,         r=-2         _____,…

A: To find the first three terms of each sequence

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: Find all values of x such that x – 7, x +7, and 8x – 7 form a geometric sequence. Give your answers…

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Q: The number sequence a1, a2, a3, .... is defined by a1 = 8 a2 = 24 and recursion formula 4an + 1…

A: We need to show that an=5n-12n-2 for a1=8 and a2=24  The given recursion formula is…

Q: What will be the sequence generated by the generating function 3x/(1-x)2?     a) 9, 12, 15, 18,……

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Q: The sequence is defined using recursion formula. Write the first four terms of the sequence: a1 = 3…

A: we have been given recursion formula : an = 4an-1 for n ≥ 2 a1 = 3  we have to write the first four…

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: Write the first five terms of the sequence with the given nth term

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Q: 17th term of the sequence 7,4, 1,......

A: For part (1) We have to find out the 17th term of the given sequence.

Q: Find the first 10 terms of the sequence an Зп + 2. its 9th term is its 10th term is

A: Given that

Q: Terms of the sequence a1, a2, a3, . .. , a2020 are obtained by the rule: 1+a1 1+ a2 1+ a2019 az = 1-…

A: Reciprocal of a number n is 1n.

Q: The sequence is defined using recursion formulas. Write the first four terms of the sequence.a1 = 4…

A: Given recursion formula, an=2an-1+3 for n≥2 a1=4

Q: Find the 10th term of the geometric sequence. aj1 = -5, r = - %3D %3D 10th term:

A: →nth term any geometric sequence is given by,                            an = a1 rn-1 , Where a1  is…

Q: Find an example of a sequence with the given property. a) xn - 3 and x, # 3 for all n. - 3 and the…

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Q: Find a closed formula for the sequence defined recursively by bo = 2, bị 3 and b 3b-1 - 2b-2 for…

A: Given sequence is given by  bn = 3bn-1 - 2bn-2 and b0 = 2, b1 = 3. So, b2 = 3*3 - 2*2 = 5 b4 = 3*5 -…

Q: Find the limit inferior and limit superior of the sequence {[5 sin n]}.

A: The given problem is to find the limit inferior and the limit superior for the given sequence of {[5…

Q: What is the 100th term of a sequence of number in which, for every positive integer x, the sum of…

A: In the given question, concept of summation series is used. Summation Series The total of the series…

Q: The sequence is defined using recursion formula. Write the first four terms of the sequence: a1 = 4…

A: The first term is a1 = 4  and an = 2an-1 + 3 for n ≥ 2

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: {sin ()} 2

A: Given sinnπ2

Q: Find all values of x such that x – 4, x + 4, and 4x – 4 form a geometric sequence. Give your answers…

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Q: 4. Find the value of x so that x+7, -x-1, x+ 13,.. shall form a geometric sequence.

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

A: We will find out the required sequence.

Q: Create your own sequence explicit formula.

A: Let, a sequence be: 2,4,8,16,32,64,... This sequence can be derived as  21=222=423=824=1625=32 and…

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: Find the formula of the Sequence. 1.) 2,1,3,4/3,15/4..., or 2, 2/2, 3/1, 4/3, 5(3)/4,...-

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Q: The sequence fn is given asf1=1 ,f2=3 ,fn+2=fn+fn+1 for n>_ 1. How many even terms are between the…

A: Calculate first few terms of the sequence, by substituting, n=1,2,3,... in the equation,…

Q: The sequence is defined using recursion formulas. Write the first four terms of the sequence.a1 = 5…

A: Given that, an=3an-1-1a1=5

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

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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: The generating function of the sequence 5,5,5,5,5 is 1-x5 O (1-x) 5 1-5x° O (1-x) 1-125x5 (1-x)…

A: We need to find the generating function of the sequence 5,5,5,5,5.

Q: Find the first six terms of the recursively defined sequence 1/2 2s n-1 Sn for n > 1, and si = first…

A: Given : A sequence  sn = 2sn-11/22 for n>1 and s1 = 1 To find : First six terms of the given…

Q: Find the first 10 terms of the sequence An 2n + 3. its 9th term is its 10th term is

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Q: 2. Write the first five terms of the sequence given by Un= on 3n2 -1

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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: Find the first 10 terms of the sequence an 5n + 2. its 9th term is its 10th term is

A: To find the first ten terms of the sequence substitute n=1,2,3,........9,10 in an

Q: The sequence is defined using recursion formulas. Write the first four terms of the sequence.a1 = 3…

A: a1=3 , an=4 an-1

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: Find the ordinary generating function for the sequence 1,1,1,1,0,0,0...(Hint: it is a polynomial.)

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Q: 2. Write a recursive definition for the sequence 14, 10, 6, 2,... Oaj = 14, an = an-1+4 %3D Oa = 2,…

A: To write a recursive defintion for the sequence 14, 10, 6, 2, ...

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: Use sigma notation to write the sum. [6 - ()°] + [6 - (4)°] +-- • [s - (2)'] k = 1

A: According to the problem, we have