A sequence is said to be an increasing sequence if ... Vn 21 .a n+1 2n.bO n+1 n+12.c0 Sn2Sn+1.dO

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: The simple formula for a, if the first 5 terms of the sequence {an} are 1, 21, 121, 621, 3121 is:…

A: We are asked to find which is correct for the sequence.

Q: Which of the following represents any term of the sequence 6 12 3 5' 2 20 30 42 56 ... ? 1' 7 9 11'…

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Q: Find the first three terms of the sequence whose nth term is given. Sn = 3n - 2 A51=1, 52 = 2, 53 =…

A: Given : sn = 3n - 2

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

A:

Q: A sequence is said to be an increasing sequence if .. Vnz1 =S .a n+1 Sn2Sn+1.b O 2n.c O n+1 .d O n+1

A: A sequence is said to be an increasing sequence if...∀n≥1 To select the correct option  Sn+1 = Sn…

Q: A sequence is said to be decreasing sequence if Vn >1 2n.a O n+1 'n²³n+1·bO n+ n+1dO n+ 1

A: Given a statement

Q: 19 Find the explicit formula for the given sequence. 2, 8, 32, 128, .. A an = 2+4 (n – 1) B an = 4+2…

A: Given sequence 2,8,32,128...... We notice that  a1=2=21 a2=8=23 a3=32=25 .......

Q: th Write an explicit formula for an, the n' term of the sequence 4, –20, 100, ....

A: We have to find nth term

Q: Write an explicit formula for an, the n'n term of the sequence 1, 5, 25, ... .

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: Prove {3n/(3n-1)} n=1 to infinity, is a decreasing sequence in R.

A:

Q: Let an be the n th element of the sequence 5,8,11,14,17,.., then an=d xn+c for constant values d and…

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Q: Determine lim a,n of the sequence (an) where n00 4 – 2n + 6n² an Зп? + п — 4

A: Given sequence is, an=4-2n+6n23n2+n-4 Now, limn→∞6n2-2n+43n2+n-4=limn→∞6-2n+4n23+1n-4n2=6-0+03+0-0 […

Q: 27.The first and 25th term of the sequence an = (-1)"-1(n – 1) are both positive. Ο Α. True О в.…

A:

Q: 7 Find the explicit formula for the given sequence. 2, 8, 32, 128, . (A 33 · 4"-1 a = = 2 · 4"-1 a ©…

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Q: 4. If a1 = 2 and az = 3 and an = an-1 + 3an-2 for n> 2, a. find the first five terms of the…

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Q: A sequence is defined by f(0) = -4, f(n) = f(n – 1)- 2 for n > 1. Write a definition for the %3D |…

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

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

A: We need to check whether the given sequence is eventually decreasing or not

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: (c) Show that the sequence is eventually strictly increasing. 13 n=1

A:

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

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

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

A: False.

Q: 12. Find the first 5 terms of the sequence: 2n a, =(-1)" n +1 a) b) a, = 4a-5 and aj =1 | n-1

A:

Q: Find an for a sequence with the 8th term 28 and the 10th term 42. а. 8n + 28 7n + 28 7n - 14 b. с.…

A: We have to find the general formula for the sequence whose 8th and 10th terms are given

Q: A sequence is said to be an increasing sequence if n+1 n+1 Sn2Sn+1 c O n+1

A: I will use the definition of increasing sequence.

Q: III Use the given nth term formula to compute the first six terms of the sequence. n2-1 1. an = 2-n…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

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: A sequence is said to be decreasing sequence if Vn 2 1 =DS n+1 aO .b O n+1 n+12s.cO 2n.d O n+1

A: Option (b) is correct.

Q: Suppose c0, c1, c2, ... is a sequence defined as follows:  c0 = 2, c1 = 2, c2 = 6, ck = 3ck-3 for…

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Q: A sequence is said to be an increasing sequence if . . Vn 21 .a O n+1 n+1 2n,c O n+1 n+1 d O n

A:

Q: Which of the followings are false? is a decreasing sequence. 1. 2" n2-1 II. is not a bounded…

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Q: (b) Let T, be the sequence of positive multiples of 13, ... .e. 13, 26, 39, ... i. Find the first…

A: The given sequence  Tn=13n:n≥1and n is a positive integer. (i) To find the first term greater than…

Q: A sequence {a n} is defined as follows: ao =2 a1 = 1 for n22,an=3•an-1-n·an-2 +1 What is a3?

A: a3=-2

Q: 1 The sequence converges to ,? – 1 – V n² +n | Select one: True 21 False

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: The sequence {n³ + 1}~, is n=0 O a. neither increasing or decreasing for all n > 0 O b. both…

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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…

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Q: The limit of the sequence an= (1+)* -- is: 3n (a) – e (b) el7) (c) e-3 (e) None a b C d e

A:

Q: 1. A sequence is defined by the recursive rule c, =c, 2" with c, =5. Which of the following…

A: Given a sequence:    cn=cn-1.2n-1          and c1=5

Q: e) Suppose {a,}nEN is a sequence defined by a, = (a) Show that a, = 3- an-1+ 2. (b) Find (dn -…

A:

Q: A sequence is said to be an increasing sequence if .... Vn 21 .a O n+1" n S =SbO n+1 n+128.cO 2n.dO…

A: sequence (an) is: strictly increasing if, for all n, an < an+1; increasing if, for all n, an ≤…

Q: 2. Which is (are) the initial condition(s) for the Fibonacci sequence? Fo=1, F₁ = 1 Fo=1 F₁ = 0…

A: We can solve this as follows:

Q: Let {an} be a positive monotonic sequence with sup an = 12345. Which of the following statements is…

A: Counter example: For option E:  {an}=12345/n for all n€Natural no.  This is positive monotonic and…

Q: c. Let a be the sequence defined by a₁ = 1, a₁ = 8, and a = a₁ +2a₂ for n ≥ 3. -1 Use an inductive…

A:

Q: Use the graphs of the arithmetic sequences {an} and {bn} to solve:If {bn} is a finite sequence whose…

A: Consider the following graphs of the sequences an and bn. From the above graph the sequence obtained…

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.

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.