Find the explicit formula of the following sequence. {8, 4, 2, 1, ...} f(n) = a, · 3n-1 a

Q: Write a formula for the nth term of a, of the sequence and determine its limit (if it exists). 1 2 3…

A: Given sequence is  13,24,35,46,57,....... It can be written as…

Q: Find the limit of the following sequence or determine that the sequence diverges. {((-1)n + 1…

A: We first divide the numerator and the denominator by n^3

Q: consider the following sequence {a,n}: 2 1, 4 8 16 32 9 13 17 21 find the formula for a, where n >1

A: A series is a sequence of numbers following a certain pattern.  Generally, we come across two series…

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: Find an explicit formula for the following sequence, a, which starts with a 3 5 7 9 2'4'6'8' Select…

A: Given

Q: 1. Find these terms of the sequence (a,), where a, = 2 (-3y"+5". %3D b) a c) as d) as a) do

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Q: For the following determine if the sequence is increasing, decreasing, not monotonic, bounded below,…

A: Check whether the sequence is increasing, decreasing or not monotonic. The given sequence is…

Q: Use all three methods, (difference, quotient, and derivative) to determine if the following sequence…

A: We can use addition or subtraction method To check whether  following sequence is increasing or…

Q: Find S, for the following geometric sequences: 1, 10 100 5,-

A: Consider the following geometric sequence: 1,110,1100... First terma=1 Common…

Q: 2n3 {(-1"ア+! 十3 n=1

A: Notes:limn→∞an exist if and only if all the subsequence converges to same limit.Suppose, limn→∞an =…

Q: In an n. formula of a sequence, the general term an is given as a function of the index

A: Recall: Arithmetic progression

Q: For the following sequence, give an explicit formula for the nth term.…

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Q: Determine whether the following sequence converges, and if so to what value does it converge? 1. 4n?…

A: find if the given sequence converges or not

Q: Find the explicit formula for the geometric sequence Cn with the following information given. c1 = 2…

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Q: Re-index each of the following sequences to start at the indicated initial index 1 no = 3 and no 12…

A: To re-index a sequence a1, a2, a3,…,an…, starting from n0=k, we change the formula by replacing n by…

Q: Suppose that we start with the sequence 1 1 1 1 1 1 '2'4'8'16'32'64' If we denote the above sequence…

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Q: Define the following sequence recursively, giving two instructions in mathematical language. {1, 4,…

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Q: Given the following sequence, provide the (unsimplified) sum of the first 20 terms: -2, 3, 8, 13,…

A: given sequence is :                                       -2, 3, 8, 13...  we have to find sum of n…

Q: Find first 5 terms of the following sequence: {an} given by a, = (-1)" („ 3n-2 n2-2n+3 99 Evaluate:…

A: First five terms of the sequence an=(-1)n(3n-2n2-2n+3) at n =1  a1=-3-21-2+3=-12 at n =2…

Q: For the following sequence, give an explicit formula for the nth term. a1=6 an=−5an−1 for n≥2

A: We have to find nth term

Q: Find a formula for the nth term of the sequence where a, is calculated directly from n. 6 10 14 18…

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Q: For the following sequence, give an explicit formula for the nth term for n ≥ 2. an 2 a₁ = 2, an+1 =

A: We are asked to find the explicit formula for the sequence.

Q: For each of the following sequences, state a formula for the general term a, where n > 1. [E.g. For…

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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: Define the following sequence recursively, giving two instructions in mathematical language. {3, 6,…

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Q: 6, V8

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Q: Find the general term of the following sequences.

A: The general term of the sequence is obtained by observing the sequence and see how the pattern…

Q: Find a function, f(n), that identifies the nth term of the following recursively defined sequence as…

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Q: What is the sequence function (an) for the following 1 2, 1.2, 3 3

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Q: The sum, Sn, of the first n terms of the sequence is given by the formula Sn =______ , where a1 is…

A: The sum, Sn, of the first n terms of the sequence is given by the formula Sn = a1(1-rn)(1-r)

Q: Find an expression for the n th term (t) in each of the following sequence: 1 1 1 1 1 >... 3 4 5 6.…

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Q: {an}= {2n– 1} {ansn=1 00 n Sn+1] {an}- {anšn=l 2n 2n {andn=1 n+1]

A: To Check that which of the following sequence is Convergent, descending and smallest upper bound 1…

Q: FInd the indicated sum for the geometric series.  1. 4+2+1+...;S10 write the first n terms of the…

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Q: Find a function f(n) that identifies the nth term a, of the recursively defined sequence, as a, =…

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Q: 5 7 9 11 13 1'2'6'24'120'

A: We need fond the pattern here

Q: Find the sum of the finite geometric series by using the formula for Sn 16 32

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

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Q: 7n*-5n³+21n+40 8n³+11n²-32

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Q: 1 1 5' 6 1 Find an explicit formula for the sequence ÷, - - 3' 4 ... 2

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Q: 2. Find a formula for the sequence given by Xn+1 4.xn - 5xn-1 + 2xn-2 n 2 2, with xo = 2, x1 = 7 and…

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Q: Use the given nth term formula to compute the first tên terms of the sequence. n(2n+1) 6. аn 3 2

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

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

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Q: 5. Consider the table and match the explicit formula that fits the geometric sequence n 1 4 f (n) a.…

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Q: SHOW YOUR SOLUTION DETERMINE THE FIRST FIVE TERMS OF EACH DEFINED SEQUENCE, AND GIVE THEIR…

A: Given, The nth tems of the sequences {3n+1} {n²-1} an=an-1+1 , a1=5 an+1=3an , a1=1 Let's assume…

Q: Find a formula for the nth term of the sequence where a, is calculated directly from n. 37 11 15 19…

A: The numerators are 3, 7, 11, 15, 19,... This is an arithmetic progression with a common difference…

Q: For the following sequence, give an explicit formula for the nth term. aj = 6 %3| An -5a,-1 for n >…

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Q: For each of the following sequences, whose nth terms are indicated, state whether the sequence is…

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Q: For the following determineif the sequence is increasing,decreasing, not monotonic, bounded below,…

A: Given:  an =e3nn=0∞ To identify the sequence:…

Q: For the following determine if the sequence is increasing, decreasing, not monotonic, bounded below,…

A: Given, e3nn=0∞ The points in this sequence are, 1, 20.085, 403.42,... Hence, The sequence is…