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 (1-x)

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

A:

Q: An arithmetic sequence has a its 5 th term equal to 22 and its 15 th term equal to 62. Find its 100…

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Q: ind the sum of the first eight terms of the sequence 1/8,−1/4,1/2, . . ..

A:

Q: Find the 11th term of the harmonic sequence1/5,1/8/1/11,1/14,. . .

A: harmonic progression is 1arithmetic progression the given series has a pattern of = 13+previous term…

Q: Find the first 6 terms of the sequence with first term8 and nth term an = an-1 + 3.

A: Arithmetic Sequence :                                          An arithmetic sequence is a…

Q: Determine the first six terms of the sequence defined by t₁ = -5 and t = -3t-1 + 8. -5, 23, -61,…

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Q: Find the first 4 terms of the sequence with first term5 and nth term an = an-1 - 2.

A: Given: The first term of the sequence, a1 =5 And the nth term,…

Q: Can you find a formula or rule for the nth term of a se- quence related to the prime numbers or…

A: The formula for nth term of sequence for given problems are given in step 2.

Q: Find the generating function for the finite sequence 2, 2,2, 2, 2, 2.

A: Step 1: Consider the provided question, Given, the finite sequence 2, 2, 2, 2, 2, 2.

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 at least three different sequences beginning with the terms 1, 3, 9 whose terms are generated…

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Q: Which sequence could be described by the recursive definition: tn+1 = -1(tn) + 3 O A. (-9, 6, -3, 0,…

A: Given recursive formula is tn+1=-1tn+3.

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 first five terms of the sequence tn = 1(1/3)n-1 are: If necessary, express terms as improper…

A: We can find the required terms as below.

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: 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: 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: 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: Write out the first 5 terms for an algebraic sequence starting with 8 with a rate of change of 4.…

A: The first term  of the sequence is 8 i.e a=8 ,and the rate of change is 4. So, let ratio between the…

Q: Suppose that the sequence {ax} is =0 2, 4, 6, 8, 10, 12, 14, 16, .. What is a1?

A: The given sequence {ak}k=0∞ is -  {ak}k=0∞ = 2,4,6,8,10,12,14,16,18,......... The first tern of the…

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

A:

Q: Write the first five terms of the sequence with the given nth term. = sin 2 %3D 4. 5.

A: To write the first five terms of the sequence with the given nth term.an=sinnπ2

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

A:

Q: Supposed vn =17-n2  is the explicit specification for a sequence. How many values of n (positive)…

A: Given: Vn=17-n2

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: Choose an expression for the apparent nth term of the sequence. Assume that n begins with 1. 1,-1,…

A: Given sequence 1 , -1  , 1 , -1 ,  1 ,  . . . . . .

Q: Find the nth term of a sequence whose first several terms are given. 3, 5, 3, 5, 3, 5, ... an =

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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: The first week, a patient engages in various exercies for 4 minutes every hour while awake. For each…

A: Explanation of the answer is as follows

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: recursively defined sequence

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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: Find the first 4 terms of the sequence with first term2 and nth term an = 2an-1 + 3.

A: Our Aim is to find the first 4 terms of the sequence with first term and nth term an=2an-1+3

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: Consider the sequence: 2, 4, 8, 16, 32, ...Determine the 13th term of the sequence.

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

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

A:

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: Find the first 5 terms in the sequence. 3.) x + 9 -8,-7,-6,-5,0 A.) י5n1 -7,-2,3,

A: First five terms of sequence

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,