Find a formula for the general term an of the sequence, then find the limit. 3 7 11 15 19 25' 125 625' 3125' 15625

Q: The limit of the sequence an = (1+±)" is: 3n) (a) – e3 (b) oG) (c) e-3 (d) eG) (e) None)

A: The given sequence is: an=1+13n-n

Q: Find the explicit formula for the geometric sequence t, given below. Note that tį = 10. 5 5 5 10,…

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Q: 1. Find the limit of the sequence if it exists: 1- n 70 - 4n? (a) a, (b) a. - (0.9)" (c) a, -…

A: Dear student. You have posted many questions. In our policy, i have answering the first question. If…

Q: Find the explicit formula for the geometric sequence t, given below. Note that tị = 10. 5 5 5 10,…

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Q: (d) How many terms does the sequence 5,9, 13, 17,21,..,533 have? (e) Find the sum: 5+9+ 13 + 17 + 21…

A: Arithmatic progression:   a1,a2,a3,...........an.....a1=first term,an=nth termd=common…

Q: 1. The general formula for a sequence is t = 3t₁ - ₁ - n, where t₁ = 3 Find the fourth term.

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Q: 1 ;, n > 3. n vIn n Let an Show that the sequence {an}-3 is decreasing.

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Q: 5 10 15 20 25 4. The sequence {÷,÷ .} converges. Find a formula for a, and find 3'9'27'81' 243 lim…

A: In the given sequence the numerator is the arithmetic sequence that has a general term an = 5n   And…

Q: Choose the correct statement(s) for given sequence 2n An n2 +1 One incorrect answer cancels one…

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Q: Write an expression for the nth term of the sequence. (Your formula should work for n = 1, 2, . ...)…

A: The given sequence is 12,13,17,125,1121,...

Q: (ii) For the sequence ) find the value of m E N , given that & 1 e 10

A: We find value of m=?

Q: The limit of the sequence a,= (1+) s: (a) – e? (b) e) (c) e-a (a) e) (e) None

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Q: Consider the sequence defined by æo = 1 and for n > 0, an+1 = v2 . xn (a) Is this an implicit or…

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Q: 2. Which one is the correct statement for the sequence that does not have a limit? VC Vn e N3e > 0 =…

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Q: 3. Let an be the sequence defined by a1 = 1 and an for - ... n > 1. (a) Calculate the first four…

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Q: a) Write an expression for the n™ term of the following sequence. b) Does this sequence converge or…

A: We have to find a) an expression for the nth term of the following sequence. b) does this sequence…

Q: For each sequence below, find the first five terms of the sequence, and then find the the limit of…

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Q: 3. A sequence is defined by the formula f (n)-S(n-1)3D15 and f(1)= 4. Which of the following is the…

A: First we will rearrange the given relation and observe the pattern that tells us that it is an…

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

A: Given, -84,1016,-1264,14256,-161024,... Here, a1=-84 a1=-112(1+3)41=-84   a2=-122(2+3)42=1016…

Q: Use the formula for the general term (the nth term) of a geometric sequence to find the indicated…

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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: The given sequence is:43, 49, 427, 481, 4243, ...To find the formula.

Q: (a) Plot the first four terms of the sequence Зn? - Зп +2 2 (b) (i) Write in bracket notation the…

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Q: c)Find the limit of the sequence a, = nsin (-) Answer:

A: Given problem:-. Find the limit of sequence an = nsin(1/n)

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

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Q: (1 2 3 4 5'8' 11'14' 1 Complete the parts below. Consider the sequence where aj (a) Find a5, a6, a7,…

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Q: Find the explicit formula for the geometric sequence tn given below. Note that t = 10. 5 5 5 10,…

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Q: Find the explicit formula for the geometric sequence an with the following information given. 4 A4…

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Q: Assume the terms of a sequence (a,}-1 are given by the following formula: 2 3 an 5n2 5n2 5n2 + 5n2…

A: Calculate the sum of the series than solve for n approach to infinity.

Q: Find the limit of the sequence; {an}n21 if: 1+2/2+3/3+.+n/ñ An choose one alternative as an answer:…

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Q: Use the difference an+1 – an to show that the sequence - {n – 6“}n=1 +0o - is strictly increasing or…

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Q: a) 29,1+ 29, 2C1+ 1) (2+9) 4+9 (i) comment whe ther the sequence is converges ordiverges (i oblain…

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Q: Assume the terms of a sequence (a,) are given by the following formula: Find the limit of the…

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Q: O Q 12. Use the function formula to find the term of the geometric sequence. 2, 8, 32, 128, ... Find…

A: We can find the 8th term as below

Q: i. Comment whether the sequence is Converges or diverges. ii. Obtain the first five terms of that…

A: We know sequence is convergent when limit of sequence is finite

Q: Consider the sequence whose nth term is a, = 3•5". Find аz аз ад a5 and 2. What do you observe? a4…

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Q: S is a gcometric sequence. (a) Given that (Vx-1), 1 and (Vx +1) are the first three terms of S, find…

A: Given data: The first three terms are, x-1,1,x+1

Q: D Find the limit of the sequence or determine that the limit does not exist. Explain your answer,…

A: As 6n+87n-1 exists and is continuous, the limit for 1≤n<5000 exists. Similarly, 5n-39n+4 exists…

Q: Write an expression for the apparent nth term (a,) of the sequence. (Assume that n begins with 1 1 1…

A: We have to find nth  term

Q: Write the terms a1, a2, a3, and a4 of the following sequence. If the sequence appears to converge,…

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

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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: The objective is to find a formula for the general term  a_n of the sequence.

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

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

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Q: Determine the explicit formula for the nth term of the sequence written below. Note that the first…

A: To determine the explicit formula for the nth term of the sequence written below.14, 13, 25, 49,…

Q: Find the limit of the sequence: бп? + 5n + 6 an 3n2 + 3n + 5

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Q: 3. A sequence is defined by the formula f (n)-f(n-1)=15 and f (1) = 4. Which of the following is the…

A: A sequence is defined by formula fn-fn-1=15 and f1=4, That is, fn=15+fn-1 Obtain pattern as follows:…

Q: The nth term of a sequence is given. Find the first 4 terms. 2n 1 %3D + 2n 5 7 3 1, OT8 15'8 7. 1 1…

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

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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: Arrange the series and make pattern

Q: For the sequence given, find the closed formula for an , the nth term of the sequence by relating it…

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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.