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 dO n+1

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: n +1 The sequence an converges to 2 - 1) n- 1 Select one: O True O False

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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: If an Is an increasing sequence and every term a, is less than 10,

A: Given:- If an is an increasing sequence and every term an is less than 10, then lim      an=10n→∞

Q: Use the difference an+1 a, to show that the given sequence {a, } is strictly increasing or strictly…

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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: 1 The sequence l(n + 4) (n+ 4) diverges Select one: 20 True False

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: 12 5n The sequence 1+ 5n n=1 Converges to

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Q: Give a recursive definition of the sequence (a), n = 1, 2, 3,. if an = 3n - 1 Choose ALL that apply.…

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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: Which is (are) the initial condition(s) for the Fibonacci sequence? O F = 0 O Fo = 0, F = 1 O F 1 O…

A: To choose: Which is the initial condition for the Fibonacci sequence. Concept used: The Fibonacci…

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: Select the first five terms of the sequence. (Assume that n begins with 1.) an = (-1)" n+11 4 5 12'…

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Q: Let (an) be a sequence such that (a)a, where a # 0. Show that la - a (3/4)a? lan-als and deduce that…

A: Given: an be a sequence such that an3→α3, with α≠0. To do: Show that…

Q: A sequence {an} is called decreasing an S an+1 for all n E N. ulgn

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Q: 7. The famous Rodrigues formula states that H, (x) = (-1)"e*² (4)" functions for positive integers…

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Q: •) TT.). Suppose that X₁, X,... is an independent sequence and Y is measurable o(Xn, Xn+, ...)for…

A: From the above details we have,

Q: A formula for the sequence 0, 3, 8, 15, 24, is Select one: О a.(п - 1) (2n -1) O b.n(2n + 1) О с (п…

A: Given sequence is 0,3,8,15,24..... Now we can write, 0=1-13=4-18=9-115=16-124=25-1

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

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

A: False.

Q: Which of the following sequences is strictly decreasing 8. n+ 1 n+1 S None

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Q: In(n + 1) In(2n + 1) J

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Q: 5. The sequence . is convergent in (R. d). a. True b. False

A: 5 -b(false)

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: A monotonically increasing sequence diverges to 00. Select one: O a. True O b. None of these O c.…

A: This question is related to monotonic sequence property.....

Q: 20. Which is (are) the initial condition(s) for the Fibonacci sequence? O F₁ = 1 O Fo=0, F₁ = 1…

A: Solve the following

Q: One of the following sequences is strictly increasing n! nn I n=1 {ne"} 00 n=1 {ne" }1 10" (2n)! n=1

A: We have to solve

Q: Which of the following sequences is strictly decreasing n+ 2 S =1 n+ 2 00 {-1)" 1n+ -1

A:

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: 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

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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: A is a sorted sequence that has length k. If k is even and A is presented as an array, the median…

A: For even sample size,  Median is given by, M={(n/2+1)th term +(n/2)th term}/2 Where n is the sample…

Q: Give a recursive definition of the sequence {a,} , n = 1 , 2, 3, ... if an 6n %3D OA. an+1 a, for…

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Q: 5. The sequence r. is convergent in (R. d). a. True b. False

A: 5 - b , (false)

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: Use the difference anti-an to show that the given sequence {a} is strictly increasing or strictly…

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Q: Which of the following represents any term of the sequence 12 20 30 42 56 7'9 11' 13 n(n+1) 1' 3 5'…

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Q: Which of the following sequences is strictly decreasing n+2 {(-1)"} n+1S -1 O None n+2

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Q: The sequence{In(n+ 1)}° is O strictly increasing O strictly decreasing O increasing decreasing

A:

Q: 1. Which of the following represents an explicit formula for a given sequence? 1. A(n) = 2 A(n − 1)…

A: The explicit formula for a sequence will depend on n. A recurrence sequence will depend on preceding…

Q: 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

A: Option (c) correct . because

Q: Which of the followings are false? I. is a decreasing sequence. n² –1 I. is not a bounded sequence.…

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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: 1. Let c > 0 be fixed and define the sequence {an} by setting an (an? + 3c) а1 > 0, аn+1 for n E N.…

A: As per BARTLEBY GUIDELINES, I answered one question(i.e, Q-1) and repost other questions separately…

Q: One of the following sequences is divergent {8}n=1 O None 2n en n=1 3n (-1)". n2 + 7 n=2 2n? +11…

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Q: One of the following sequences is divergent 3n (-1)n n2 + 7 n=2 3. n=1 (-1)* n=1 O None

A: