The sequence an is eventually decreasing n! Select one: O True O False

Q: A sequence is said to be decreasing sequence if Vn > 1 'n+1°n =S .a .b O n+1 2n.cO n+1 n+1d0 n

A: Option (d) is correct.

Q: Express the sequence {an}∞n = 1 as an equivalentsequence of the form {bn}∞n = 3. {n2 + 6n - 9}∞n = 1

A: Given

Q: The third term in the sequence with a=4 and a = a + 3n wheren>1 is %3D O 22 0 4 O 13 O 10 O 19

A:

Q: The limit of the sequence a, = (-1)"2 is equal to %3D Select one: True O False

A:

Q: Which explicit formula describes the geometric sequence {1/3,1/9,1/27, 1/81…}? A. an= 1/3 (3)^n-1…

A: Given sequence is: 13,19,127,181, ...

Q: A sequence is said to be decreasing sequence if...... Vn>1 =S b O n+ 1 n n+1C O S 2n.d O n+1

A: Correct option :-  C Detailed Explanation

Q: Select the first five terms of the sequence. (Assume that n begins with 1.) an = (-1y"| n+11

A: Substitute n = 1 and 2  and then find a1 and a2.

Q: An arithmetic sequence is defined as consecutive terms that have a common difference. O True O False

A: NOTE: Refresh your page if you can't see any equations. . the nth term of the arithmetic sequence is…

Q: In a(n) _____  sequence, the ratio of successive termsis a constant.

A: A sequence in which ratio of successive terms is a constant is called a geometric sequence. Consider…

Q: Use the given table to write an explicit and a recursive rule for the sequence. 2. 3. 1 3 4 1 2 3 4…

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

Q: (b) Generalize: if the numbers 1 to n are placed around a circle in some order, what is the best…

A: (b) If the numbers 1 to n are placed around the circle in some order, the best possible lower bound…

Q: The third term in the sequence with a1 3 and an = an-1 + 2n where n >1 is

A:

Q: Write an explicit formula for the sequence: 1 1 11'12' 1 1 9' 10 1 13

A:

Q: A sequence {am} is called increasing, if an > an+1 for all n > 1. Select one: O True O False

A: We can answer it as below as per the definition of increasing function.

Q: Which explicit formula describes the geometric sequence { 1 1 1 3' 9 27 ' 81 .. n-1 an=+(n- 1) ()…

A: The given sequence is: 13,19,127,181,... That is: 13,132,133,134,... So, the general form of the…

Q: Solve for x & y if the given sequence is arithmetic Зх + 6у, 4у, 7х + 2, 2х — 3у

A: Explanation of the answer is as follows

Q: Which of the following is the value of x to make x + 1, 4x – 7, 2x + 5,… an arithmetic sequence.

A: We will find the value of x for which the given sequence will be  an arithmetic sequence as…

Q: Find the 20th term of the sequence s, = (-1)"(n + 1).

A: Givensn=(-1)n(n+1)

Q: Find the first four terms of the sequence defined recursively. an-1 ). a¡= -1, an= 3an-1 11. a¡ = 5,…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: th Write an explicit formula for an, the n" term of the sequence 2,-5,-12, ....

A: Given:2,-5,-12,.......Given sequence is in A.Pa=2…

Q: Write an explicit formula for the sequence: 1 1 12' 13 -1 1 8'9' 1 1 | .. 10' 11

A:

Q: Use a-a, to show that the given sequence {a,} is strictly increasing or strictly decreasing. b)…

A:

Q: Express the sequence {an}∞n = 1 as an equivalentsequence of the form {bn}∞n = 3. {2n + 1}∞n = 1

A: 2n+1n=1∞ When n=1, a1=21+1=3 When n=2, a2=22+1=5 When n=3, a3=23+1=7 When n=4, a4=24+1=9 Therefore…

Q: Compute the first 6 terms of the sequence {an} where An-1+n a1 = 1 and an for n > 2.

A: The given sequence,a1=1 and an=an-1+n2 for n≥2

Q: Which of the options is correct for the following sequence: 4n

A: here last option is true because if be put n=1 than value is 1/4  and take limit at n->infinite…

Q: Choose the correct statement(s) for given sequence 2n an n2 +1

A: a sequence is converges if  limn→∞     n = finite

Q: The sequence n-21 is divergent. True False

A: We have given a sequence  ,   n-2. We need to determine sequence is convergent or divergent. We know…

Q: 1 Find the twentieth term of the sequence an = 2 ( 0.1 )"

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

Q: A sequence {an} is called monotonic, if it is neither increasing nor decreasing. Select one: O True…

A: False.

Q: Let an Determine if the sequence is monotonic or not. (n+1.

A:

Q: Let an be a sequence defined by a1 = 0 and a2 = 1 and for n > 3 an = (n – 1)(an-1+an-2). %3D

A: Here, the terms given in the series are, a1=0,a2=1an=n-1an-1+an-2 Calculate the third, forth and…

Q: Write out the first four terms of the sequence given the following recursive definition: tne1 =…

A: # the given initial value is a1=8 . considering it as t1=8 given the relation tn+1=-2tn+6 substitute…

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

A:

Q: Ind the first four terms of the sequence given by the following. q=(-1)^2n², n = 1, 2, 3, ...

A: Given: Sequence is an=-1n·2n2. To find: First four terms of the sequence.

Q: Write the first four terms of a sequence given the following information: a: = -2 and the recursive…

A:

Q: Find the formula of the general term an of the sequence 1 1 1 1 3 '5'7 '9

A:

Q: c) Write the explicit formula for the nth term of the sequence below. d) Prove that mathematical…

A:

Q: > The general term of the sequence 1, 2' 4 , starting by n=0 is .. +00 (i) n+1 +00 (ii) (iii)None of…

A: In the question it is asked to solve for the general term of the sequence given in question.

Q: The sequence an 3" =- is eventually increasing %3D n! Select one: O True O False

A: Given sequence

Q: Which of the following sequence is divergent? {=} en n (-1)"+1 n n? l n +1] {-3}

A:

Q: Use the difference an+1 an to show that the sequence {n – 11"} is strictly increasing or strictly…

A:

Q: A sequence is said to be decreasing sequence if Vn 21 ....... 'n+1 .a O .b O n+ 1 n Sn+12n.c O O p…

A: We need to find condition in which a sequence is said to be decreasing. The answer to the question…

Q: A sequence is said to be an increasing sequence if Vn 21 ......... n+1 a O 25,00 n+1 zn.c O n+1 S =S…

A:

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: The sequence an = {nn} is eventually decreasing %3D Select one: O True O False

A: We call the sequence decreasing if an >an+1 for every n.   an = n1/n an+1 = (n+1)1/n+1   n1/n…

Q: Find the first six terms of the piecewise sequence: S( - 2)" (– 2)" – 3 if n is even an = | 3-1 – 4…

A: n=1 , 3 , 5 are odd, so we use the second piece

Q: Find the formula of the general term an of the sequence: 1 1 1 1 9' רי 5' 3 ....

A:

Q: Use the difference an+1 - an to show that the sequence {n – 9"t0 Sn=1 is strictly increasing or…

A: Topic   Function decreasing and increasing  Given function is strictly decreasing.

Q: Find all the terms of the finite sequence. 6) an = n²-n for 1≤n=5

A:

Q: Find a closed formula for the sequence (Cn)neN defined as follows: if n = 1, Cn = if n = 2, 8. Cn-1.…

A: As per the question we are given a piece-wise defined sequence (cn) and we have to find a closed…

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.