33. Study the sequence (un) defined by 3 (a) uo = a E R, Vn E N : un+1 = un.

Q: 4. for the recursivley defined sequence: Σα Find Ea; an=3an-1-2n for n22

A: The expression ∑i=14ai can be expanded as follows. ∑i=14ai=a1+a2+a3+a4   It is provided that a1=4 .…

Q: The 2 – tail of the sequence Y = (1, 3, 5, 7, 9,... , 2n – 1, . ..) is: O Y = (7,9,..., 2n + 5, ...)…

A:

Q: Which of the following is the limit 00 of the sequence {a,},where an = 3? 3 8

A: The objective of the question is choose the correct option.

Q: 1. Write the first five terms of the sequence defined by i) a, = (-1)"+1 Li. ii) b, = . 2. Find a…

A: Given: Question 1(i)  an=(−1)n+11+nn!(ii)  bn=2nn!find five termsQuestion 2(i)…

Q: Ke Find the matrix M of the linear transformation T : R → R° given by - (E) I -6x1 + x2 + 7x3 -6x1 +…

A: Solution

Q: Consider the sequence given by bn = [1 + (-1)"] for ne N. 00 (a) List the first seven terms of this…

A:

Q: 16.Consider the first 3 terms of the sequence a, (where k 2 2). A. Give the first 3 terms of the…

A:

Q: Suppose that ho, hị, h2, . is a sequence defined as follows: ho = 1, h1 = 2, h2 = 3, %3D hy =…

A:

Q: Consider the sequence {ax}, defined by а, 3D 1, ад — 1, and ak 3 а-1+ ak-2 for k > 3. Compute as.

A: We have given two terms of sequence {a_k}, a_1=1 and a_2=1 and then sequence {a_k} is defined by…

Q: The sum of the first 20 terms of the sequence 0.7, 0.77, 0.777, ... is

A: The given sequence is 0.7,0.77,0.777,...... The sum geometric sequence with common ratio r<1 ,of…

Q: List the first six (6) terms of each of the following sequences.  an=2(3n)+3, where n=1,2,3,……

A:

Q: 10. Let (an) be the sequence defined recursively by, a1 = –1, a2 = 7, for n > 3, an = аn-1 + 2ап-2.…

A: It is required to show that, an=2n+3(-1)n for all n.   Let us check for n=1.   a1=21+3(-1)1 -1=2-3…

Q: The sequence shows the total number of rodents in an abandoned warehouse at the end of each month…

A: Given the sequence is 16, 24, 36, 54, 81,  …

Q: write down the first five terms of each sequence

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find a formula for the sequence

A: In this question, we have to solve the third-order difference equation in general form and then…

Q: Write an explicit formula for the sequence: 1 1 1 1 1 [1 3 4'5' 6'7' 8 an - ...

A: Given:- (1/3), (-1/4), (1/5), (-1/6), (1/7), (-1/8)

Q: (b) Give a recursive definition of the sequence {dx},k =1, 2, . .. if (a) dk = 4k – 2; (b) dɛ =…

A: According to the guidelines, I am solving a,b and c part only.But part d can also be solve using…

Q: What is the sum of the sequence E(1+k!) R-0

A:

Q: What would be the 31 st term of the sequence x2, x, 1 А. х28 1 В. x26 C. x28 1 D. x33

A: A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where…

Q: 4. Give a recursive definition of the sequence an if an = n(n+1), where n = 1, 2, 3, ... %3D

A: We have to give a recursive definition of the sequence an where an=  n(n+1) for n= 1,2,3,....

Q: 1. Let the sequence defined by (5" +7") be given. Show that the sequence is (a) bounded and…

A:

Q: 10. If a = 2a., and a, = 3, find a formula for the sequence . (A) 6 (B) 3 x 2 (C) 2 x 3 (D) (3 x 2)"…

A: Givenan=2an-1 and a0=3 We are required to find the value of an

Q: 12. Suppose the sequence ao, aj, a2, a3, ... is defined as follows: ao = 0, aj = 1, and for n > 2,…

A:

Q: 2.152.All the expressions of an arithmetic sequence (a,) are positive and different from each other.…

A: Given : all the expressions of an arithmetic sequence an are positive and different from each other,…

Q: 8. Consider the sequence {an} such that an+1 = -3 – 2an. Then lim an = -1.

A:

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: 1 Let xn=G, 2+-), nEN be a sequence in R?, then lim x, .A (0,2) .B [0,2] .C (2,3) .D (0,2]

A:

Q: 2+(-1)" n 3. Find the LUB of the sequence: n n=1 1 b. 2 3/2 d. 3 e. 0 а. с.

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.