The first term of a converging sequence {an} is given by, a1 = 0 and the remaining terms can be generated using the following recursive relation, An+1 = /6an + 55 Find the limit of the given sequence.

Q: Find the limit of the following sequence or determine that the sequence diverges. {100(-0.003)n}

A:

Q: Find the limit of the sequence with the given nth term.  an = 6 + 2/n2

A: Given sequence is an=6+2n2. If ∑n=1∞an converges, then limn→∞an=0.

Q: Find the limit of the sequence with the given nth term. n + 5

A: Given sequence is an = (n+5)/n

Q: Determine the limit of the following sequence: 5n-5 Un бп-6

A:

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: The sequence with general term an = (-1)" is divergent. True False

A: The given sequence is divergent.

Q: Find the limit of the sequence with the given nth term. 3n + 5 an 3n

A:

Q: determine the limit of the sequence or show that the sequence diverges.

A:

Q: Find the limit of the following sequence or determine that the sequence diverges. {5(-1.01)n}

A:

Q: Find the limit of the sequence as n approaches infinity: 3n - 5 an Зп + 4

A: Given,            an=3n-53n+4To find: The limit of the sequence as n approaches infinity.

Q: Find the limit of the sequence with the given nth term. 5n + 7 5n

A: we have givenan =5n+75n

Q: Find the limit of the fallowing sequence if it exists 92 = 12-2, an =/2-/2+12+2+..+2 ' n eN

A: Explained below

Q: Find the limit of the following sequence or determine that the sequence diverges. {2n + 13-n}

A: The given sequence is {2n + 13-n}.

Q: Find the first three terms of the sequence whose nth term is as follows:

A: A sequence is a set of numbers that has a particular order or obeys a general form. The nth term of…

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: Suppose you know that  {an} is a decreasing sequence andall its terms lie between the numbers 5 and…

A: Given: {an}is a decreasing sequence & all the terms of sequence lies between 5 & 8. To…

Q: In the given equation as follows , determine whether the sequence with the given nth term is…

A: The given sequence is  an=32n

Q: Evaluate the limit of the sequence or state that it does not exist. an = n - √(n2 - 1)

A: Given sequence is an=n-n2-1.

Q: Find the limit of the sequence with the given nth term. an = n + 3/n

A: We are given

Q: Find the limit of the sequence or show that the sequence diverges. 4/x An = (3e2x + 10)*

A:

Q: Find the limit of the following sequence or determine that the sequence diverges. 11 +

A:

Q: Find the limit of the sequence or determine that the limit does not exist. n! an= 4n.7n

A: Consider the given sequence, an=n!4n·7n

Q: Compute the limit of the sequence given recursively as follows. If the limit does not exist, enter…

A: To determine the value of the limit.

Q: Find a closed formula for the sequence defined recursively by bo = 2, bị 3 and b 3b-1 - 2b-2 for…

A: Given sequence is given by  bn = 3bn-1 - 2bn-2 and b0 = 2, b1 = 3. So, b2 = 3*3 - 2*2 = 5 b4 = 3*5 -…

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

A: Given sequence is an+1=10an-1, a0=0 Substitute n=0,1,2 and 3 and use the values of previous terms.…

Q: This is sequence and the is equal to

A:

Q: The sequence is defined using recursion formulas. Write the first four terms of the sequence.a1 = 2…

A: a1=2 , an=5an-1

Q: The sequence is defined using recursion formula. Write the first four terms of the sequence: a1 = 4…

A: The first term is a1 = 4  and an = 2an-1 + 3 for n ≥ 2

Q: Find the limit of the sequence with the given nth term. 3n + 4 a in 3n

A:

Q: Find the limit of the sequence with the given nth term. бл + 5 a 6n

A: we will find the limit of the given sequence.   We know  ,  1/Infinitive  = 0 .

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

A:

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

A:

Q: Find the limit of the sequence defined by an n + 1 %3D 4"

A: The given sequence an=n+14n

Q: If the sequence ~ 9- an - 3 :} converges to 6, then the sequence {an} converges to 9.

A:

Q: The sequence is defined using recursion formulas. Write the first four terms of the sequence.a1 = 5…

A: Given that, an=3an-1-1a1=5

Q: determine the limit of the sequence or show that the sequence diverges.

A:

Q: Find the limit of the sequence with the given nth term. Зп + 8 an 3n

A:

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

A:

Q: Find a closed formula for the sequence with recursive definition An = 2an-1 – an-2 with a1 = 1 and…

A: The closed formula for a sequence is used to define the general term of a sequence. The recursive…

Q: Find the limit of the following sequences or determine that the sequence diverges. {√(n2 + 1) - n}

A: an=n2+1-n Now,…

Q: Find the limit of the sequence whose nth term is an = (1+1/ n)n .

A: We have to find the limit of the sequence whose nth term is: an=1+1nn Finding limit of the sequence,…

Q: If the sequence { 2 9 - An An - 3 converges to 6, then the sequence {an} converges to 9.

A:

Q: The term of an infinite sequence is 2n^2-n. Write the first six terms of the sequence and explain…

A:

Q: For the sequence defined by:

A: we have been given the (n+1)th term of the sequence. Given: a1=4an+1=2an+2we have to find a2,a3,a4.

Q: Find the fifth term in the sequence that is defined as follows: an = 4 + (-1)" Enter

A:

Q: The sequence is defined using recursion formulas. Write the first four terms of the sequence.a1 = 3…

A: a1=3 , an=4 an-1

Q: Find the limit of the following sequences or determine that the sequence diverges.

A: Consider the provided expression, e3n+4n Find the limit of the following sequences. Let y=e3n+4n We…

Q: Assume that the recursively defined sequence converges and find its limit. a, = - 17, an + 1 = /35 +…

A:

Q: If the sequence { 2-4 an an+2 } converges to 7, then the sequence {an} converges to 9. True or…

A:

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.