9. a) The formula for the nth term of the sequence n(n+1)(2n+1) 1, 5, 14, 30, 55, 91,... is 6 Find the 20th term.

Q: For the sequence 1, 4, 7, 10, .. . its nth term is

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Q: For the sequence defined by: ai = 3 1 + 4 An ап +1

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Q: (– 1)"9 - For the sequence an n2 its first term is its second term is its third term is its fourth…

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Q: Suppose a, is the sequence such that a, = -3 - (-1)". Find 25 Li-5 đị. O a. 325 - 35 O b. -3 Ос. 3 O…

A: Given sequence is an=−3⋅−1n. We have to find the ∑i=525ai.…

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

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Q: 30. аn e4n/(3n+9)

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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: 1. Consider a sequence that begins with 1, 4, 8, Explain why each of the following could be the next…

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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: 4 8 Suppose the sequence {b1, b2, b3, ...} is given by {-1, , 9' 27 Which, if any, of the following…

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Q: Suppose that a sequence is defined as follows. a1=-4,   an=3an-1+7 for n>2 List the first four…

A: Given: The given sequence is defined as, To determine: The first four terms of the sequence where

Q: 12 Indicate a general rule for the nth term of this sequence. 6m, 3m, 0, -3m, -6m, . . . a n =…

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Q: For the sequence an an –1+ an – 2 and a1 = 5, az = 6, = | its first term is its second term is its…

A: Given : The sequence an = an-1 + an-2 To find : First term, second term, third term, fourth term,…

Q: 1. Write down the first six terms of the Fibonacci sequence defined by Fn= Fn-1+ Fn-2, when F1=0and…

A: This question related to fibonacci sequence and pascal's triangle. Solution is given below.

Q: 13. What is the twelfth term in the sequence an = 3n - 22? 09 0-7 O 14 O26

A: Find the twelfth term

Q: If a(n) = 1/((n)*(n+1)), what is the 5th term of the sequence. Here, n is a positive %3D integer.…

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Q: 1) Assuming that the pattern of the first few terms continues, find a formula for the general term…

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Q: 11. Consider the sequence of sums 1, 1 + 2, 1 + 2 + 3, 1+2+3+4,1+2+3+4+5, .. (a) What happens to the…

A: Consider the sequence of sums 1, 1+2, 1+2+3, 1+2+3+4,.....  a) What happens to the terms of this…

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: 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: 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: Predict the general, or nth term, an, 3, 6, 9, 12, 15, ... O A. 3n OB. +3 OC. n³ O D. 4n of the…

A: Here, the given sequence is: 3,6,9,12,15,...

Q: 1. Give the first five terms of the sequence with the given general term. a. a, = 3n+4 %3D b. а,…

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Q: See image

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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

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Q: For the sequence defined by: ai = 2 1 + 5 An аn + 1 — Find: a2 az = a4 = II

A: To find  a2 , a3 , a4  substitute n=1,2,3 respectively  in the given equation.

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

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

Q: For the sequence an = An –1+ an – 2 and a1 = 3, az = 4, its first term is its second term is its…

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Q: 1. Consider a sequence that begins with 1, 4, 8, Explain why each of the following could be the next…

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Q: 1. Find the general n th term of the following sequences. 14 9 16 a) 10'17 b) -, 125, -625 ...} 24

A: Given

Q: If a(1) = 2, and a(k) = 5a(k-1) for all integers k >= 2, then what is the 4th term of the sequence?

A: A sequence is a set of numbers that has a particular order or obeys a general form. Usually, the nth…

Q: 2: Assume that the patterns shown by the square tiles in the following figure continues. What is the…

A: Given that:   There are 5 pattern shown in the given figure, and find the total number of tiles in…

Q: Give an explicit formula for an, the apparent   nth term in the sequence 7, 17, 7, 17, 7, 17...

A: .

Q: A. what is the 3rd term of the sequence defined by an=(-2n)n? B. What is the sum of the sequence…

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Q: a) The formula for the nth term of the sequence n(n+1)(2n+1) 1, 5, 14, 30, 55, 91,... is 6. Find the…

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Q: B. Use inductive reasoning to predict the next three items in each list. Make a conjecture for the…

A: B) 1. The given sequence is 1, 3, 6, 10, 15, . . .This sequence follows the pattern as +2, +3, +4,…

Q: 1. The first term of an arithmetic sequence is equal to 200 and the common difference is equal to…

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Q: 7. Identify the first five terms for each of the following sequences. (a) a, = [n/2] for n > 0 (b)…

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Q: Write out the first 5 terms (starting with ao) of each of the sequences described below. Then give…

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Q: 1.) Show that the sequence 2,11, 20, 29, ... is arithmetic.

A: we have to show that the given sequence is arithmetic

Q: 6. Write down the first 8 terms of the Fibonacci sequence and if F, is the nth F. for n = 7, 8, 9. .…

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Q: 7. How many terms are there in the sequence 1,4,7,10,...,682?

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Q: 1 Consider the sequence an = 2- n ≥ 1. 1 n²+ n4+: 4 Show that √a₁ + √₂ ++√√a119 is an integer.

A: Details solution explain with  calculation

Q: a. Find an explicit formula for the sequence 1,-4,9,-16, ... b. Determine the first four terms given…

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Q: 1. Find the 100th term and nth term of the sequences a. 0, 13, 26, ... b. 4, 16, 64, ...

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Q: In(n+74)105 In(50+190 n )109 The sequence is and its limit is n=1

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Q: 1. Write down the first six terms of the Fibonacci sequence defined by, when. (Show your solution.)…

A: Please note that as per our guidelines if the student posts multiple questions we can answer the…

Q: 10. Is there a pair of integers (a, b) such that a, x1, Y1,b is part of an arithmetic sequences and…

A: We have to find out that is there a pair of integers a,b.

Q: Consider the infinite sequence grated by 4n/ n+7 A. Determine if the sequence is…

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Q: 2. Find the recursive formula for the following sequence: 2, 5, 10, 17, 26, ... an

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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.