Find an explicit formula for a sequence of the form  a1,  a2,  a3,     with the initial terms given below 0, -1/2, 2/3, -3/4, 4/5, -5/6, 6/7

Q: Find a simple, closed form for the generating function of the sequence defined by a, n2. %3D

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Q: Find an explicit formula for the sequence defined recursively such that a₁ -4 and an = an-1 + 6.

A: We have to find the explicit formula

Q: Find a formula for the general term a, of the sequence, assuming that the pattern of the first few…

A: We need to look the pattern of given sequence to find general solution

Q: Write an explicit formula for an, the nh term of the sequence 5, –1, –7,.... -

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Q: Find the first five terms of the explicit arithmetic sequence. an = 4n 2 %3D O 2, 3, 4, 5, 6 O 6,…

A: we have to find the first five terms of the explicit arithmetic sequence an=4n-2 .

Q: Find the partial sum Sn of the geometric sequence that satisfies the given conditions. a = 8, r = 2,…

A: Given: a=8, r=2, n=6

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: Find the sum of the first five terms of the sequence with the given general term. an = (-1)"

A: general term  an = (-1)n

Q: Find a formula for the general term a, of the sequence, assuming that the pattern of the first few…

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Q: Determine the generating function for the following sequence: (),-), (2),,(-1)" (a),.. where a is a…

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Q: Find a simple, closed form for the generating function of the sequence defined by an = n².

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Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…

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Q: Find the sum (to the nearest hundredth) of the first 17 terms of the sequence defined by the…

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Q: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

A: Given : -1,-5,-9,-13,-17

Q: Calculate, to four decimal places, the first ten terms of the sequence. 3n 1 + 4n an =

A: Given, an=3n1+4n

Q: Find the closed-form of the generating function of the following infinite sequence: (2, 4, 8, 16,…

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Q: Find the first term of the geometric sequence from the given information. Express the term as an…

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Q: Find an explicit formula for a sequence of the form  a1,  a2,  a3,

A: According to the question, the initial terms of the sequence are: 0,-12,23,-34,45,-56, and 67   The…

Q: find a formula for the nth term of the sequence. 0, 1, 1, 2, 2, 3, 3, 4,...

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Q: Write a formula for the nth term of an of the sequence and determine its limit (if it exists).…

A: The sequence is: 1, -22, 34, -48, 516, ..... This can then be written as:

Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…

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Q: 1,0,

A: Given: The sequence is 0 , 1-e11+ e2 , 1- e21+ e3 , 1- e31+ e4  , 1- e41+ e5 , .  . .

Q: The first two numbers in a sequence H are H(1)=2 and H(2)=6. If H is an arithmetic sequence, write…

A: Given : H1 = 2H2 = 6 H is an arithmetic sequence.

Q: The first 4 terms in the sequence defined by the formula a; (-1)*+1 5 for i >1 a2= az = a4 =

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Q: Find the third ,fourth and fifthterms of the sequence defined by a1=2,a2=3 and an=(-1)nan-1+an-2

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Q: the sequence {12, 4, −4, −12, −20, } assuming that the pattern

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Q: Find an explicit formula for a sequence of the form a,, az, a3 with the initial terms given below.…

A: To find  An explicit formula for a sequence of the form with the given initial terms.

Q: Find a closed formula in terms of n for the sequence an described by ao = 4, and a, = 5a, –1+ 3 for…

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Q: Find the Third,fourth and fifth term of the sequence defined by a1=2,a2=3, and an=(-1)an-1+an-2

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Q: Find an explicit formula for the sequence of the form a1, a2, a3, . . . with the initial terms…

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Q: Find a formula for the general term an of the sequence, starting with a1.{3,−3,3,−3,…}.

A: Given sequence is,

Q: Find an explicit formula for a sequence of the form a,, a,, az, ... with the initial terms given…

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Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…

A: Given : 1, 4, 7, 10, 13…

Q: Find an explicit formula for a sequence of the form a,, a,, a3, with the initial terms given below.…

A:

Q: Find the partial sum Sn of the geometric sequence that satisfies the given conditions. a = 7, r = 2,…

A: Given that first term a=7, common ratio = 2 , number of terms n=5   Then we will use the sum formula…

Q: Find a formula for the nth term of the recursively defined sequence where a, =1, an+1 an for n21. 4"

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Q: Find the closed form of the generating function for the sequence 2,4, 8, 16, 32, ...

A: Generating Function: Let a0, a1, a2, a3, a4, .....be a sequence of real numbers denoted as an Then a…

Q: 5. a; = 9 and an= 3an-1-1, for n> 1

A: Topic :- Sequence and series  First three terms 26,77,230,.......

Q: 9. Find the explicit formula for a sequence satisfying а, %3D10а,, + 25а, _,n22 n-1 а, %3D 3, а,…

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Q: Find the fifth term in the sequence that is defined as follows: an = n² + 2

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Q: Find the formula of the general term an of the sequence:

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Q: Explicitly calculate the first six val- ues of the factorial sequence using the formula ao = 1 ап —…

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Q: Find a formula for the n th term of the sequence an whose first five terms are 0, 2, 6, 12, 20?

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Q: 1. Find an explicit formula for the general term of the given sequence: 5, 10, 20, 40, 80,…..

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find an explicit formula for a sequence of the form a,, a,, az, with the initial terms given below.…

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

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Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…

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Q: Find an explicit formula for the general term  an  of the sequence. 1, −  1 3 ,   1 5 , −  1 7 ,…

A: We have to find the formula of general term.

Q: Find the first four terms of the sequence defined by a, = 3 a, = 3a, -1 +2, for all n > 1

A: Given : a1=3an=3an-1+2

Q: Find a formula an for the nth term of the arithmetic sequence whose first term is a1 = −3 such that…

A: Our Aim is to find a formula an for the nth term of the arithmetic sequencewhose first term is a1=-3…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.