1-Find a closed form for the generating function for the sequence {a where a = n+2". %3D

Q: For the sequence an = n +1' its first term is its second term is its third term is its fourth term…

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Q: Find the generating function for the sequence 1,−2,4,−8,16,….

A: The general expansion of the binomial (1-x)-1 will be, (1-x)-1=1+x+x2+x3+….

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: a. -10, 30, -90, 270, -810 b. -13, -16, -19, -22, -25 c. -10, -13, -16, -19, -22 d. -10, -7, -4, -1,…

A: To find the first five terms of the given sequence.

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: Let (a,) be the sequence defined by a¡ = 5 and a, = 2a,-1 – 3 when n > 2. What is a4?

A: Here an be the given sequence which is defined by a1=5 and an=2an-1-3 when n≥2 . We have to find a4…

Q: write the first five terms of the sequence whose general term is  an=3(n!)

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Q: 5. (i) Determine the sequence gnerated by the following generating functions: (ii) e(1+x) t (1-1)³

A: (5) (i)          Given generating function is t1-t3= t 1-t-3…

Q: 3. Express the following sequence in the form {a,} Term of Sequence 3,5,7.. Formula Notation a, =…

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Q: Find the sum of the first 45 terms of an arithmetic sequence whose general term is given by 15 + 5n

A: Given that the general term arithmetic sequence is 15 + 5n.  And we have to find out the sum of…

Q: onsider the sequences 2, 5, 12, 29, 70, 169, 408, . . . (with a0 = 2). (a) Describe the rate of…

A: Given  sequences 2, 5, 12, 29, 70, 169, 408, . . . (with a0 = 2). We have to give solution for  (a)…

Q: Find ai for the sequence with generating function, 1-x 1 x x

A: Simplify the generating function.

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: Find the generating function for the finite sequence 1, 4,16, 64, 256.

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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: 1. Find the lowest degree polynomial that generates the sequence {pn} given by 2, 9, 20, 35, 54,…

A: Given sequence, 2, 9, 20, 35, 54, 77... p1= 2 p2= 9 p3= 20 p7= 104

Q: The sequence (c} diverges.

A: To check whether the sequence diverges

Q: an = {-5,–1,3,7,11, ... }

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Q: 6. Find the 25th term of the sequence -1, 3, 9, ... -

A: The formula for nth term of a GP is given as follows where a is the first term of GP r is the common…

Q: Find the sum of first 24 terms of the list of numbers whose nth term is a = 3 + 2n

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Q: 2 3 4 5 1'2' 4'8'

A: topic - formula for sequence