For each of the following sequences: • identify if the sequence is arithmetic, geometric or quadratic1. Justify your response. • Assuming the first term of each sequence isa1, give an expression for ai. (In other words, find a formula for the i-th term in the sequence). • if the sequence is arithmetic or geometric, compute the sum of the first 10 terms in the sequence. Show your work. If the sequence is quadratic, then show the work used to compute your answer to the second bullet. (a) 3,15,75,375, ... (b). 0,4,11,21, ... (c) -6,1,8,15, . ..

Q: Find an explicit formula for the sequence defined recursively such that a₁ -4 and an = an-1 + 6.

A: We have to find the explicit formula

Q: For the sequence defined by: a1 = 2 5 - 1 an+1 = Find: a2 az = a4 =

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Q: Write an explicit formula for an, the nh term of the sequence 5, –1, –7,.... -

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Q: d.Write only the first 4 terms in the sequence defined by the formula given below: k az = 2 for all…

A: First four value is  0 ,0 ,2 ,2

Q: Find a formula for a, for the arithmetic sequence. 5 aq = 0, d = - %3D

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Q: Find the first 4 terms of the recursively defined sequence. a1 =-3, an+1= an+9

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

A: Here we have to write an explicit formula for an  In the given sequence    a1 = 4 , a2 = -20 , a3 =…

Q: Determine the explicit formula for the following sequences. 4. Sequence: }, ,7, 3, 4, ... a, = } and…

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Q: Find the first four terms of the following recursively defined sequence. bk = bk - 1+ 7k, for each…

A: Since given sequence is bk=bk-1 + 7k, for each integer (k>=2) b1=1 we have to find first four…

Q: Write down the first five terms of the following recursively defined sequence. a1 = 1; an+1 = – 2an

A: Gven,          The recursive sequence is defined by          a1=1 ; an+1=-2an-2

Q: For the sequence defined by: a1 = 4 - 2 an an+1 Find: a2 : = az a4

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Q: Define the following geometric sequence recursively, giving two instructions in mathematical…

A: We have 2 , 4 , 8 ,16 ,32, ... Now, we need to obtain a recursive sequence that can define this…

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: Find an explicit formula for the following sequence, an which starts with a1=−1.…

A: We have to solve given question.

Q: Given the explicit formula for a sequence, find the first five terms and the 52nd term. 1) а — 41-…

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Q: Find the 7th term in the sequence with the following definition: a₁ = 64 an = an-1

A: Given.

Q: 1. Find the 10th term of the arithmetic sequence in which aj = 12 andd = 9.1. O a10 = 103.9 O a10 =…

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Q: Find a formula an for the nth term of the arithmetic sequence whose first term is a1 = −6 such…

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Q: An ontario lottery has the following structure,the first person drawn from the names wins $15000.…

A: We will find out the required values.

Q: The first two numbers in a sequence H are H(1)=2 and H(2)=6. If H is an arithmetic sequence, write…

A: Given : H1 = 2H2 = 6 H is an arithmetic sequence.

Q: Suppose that a sequence is defined as follows. a1 =-4, a,= 3a,-1+7 for n22 %3D List the first four…

A: A sequence is defined as follows:- a1=-4, an=3an-1+7 for n≥2 Then for n=2: a2=3a1+7…

Q: Write down the first five terms of the following recursively defined sequence. a1 = 3; an+1 = -2an +…

A: The solution is given as

Q: Consider the following sequence 4/7, 9/14, 5/7, 11/14, ____, if arithmetic, give d. and supply…

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Q: Given that a is an arithmetic sequence, a1=6 and a10=60, what is a21?

A: Given arithmetic sequence in which we have a1=6 and a10=60. To find: a21 Solution: In arithmetic…

Q: The following sequence is geometric: -1, 1, -, . O True O False

A: Given the geometric sequence−1,12,14,−18

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: Find the first 4 terms of the recursively defined sequence. a =3, a2 =4, an +1=an + an-1

A: Topic- recursive sequence A3 =7

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: 11. In a geometric sequence, if a2 = 21 and az = 5103, find a and r. Make sure to use the…

A:

Q: find the third fourth and fifth terms of the following recursive sequence

A: 11. The recursive sequence is An=2An-1-An-2, A1=4, A2=8. The third term is,…

Q: Write down the first five terms of the following recursively defined sequence. a1 = 5; an+1=-2a, – 8…

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Q: Define the following sequence recursively, giving two instructions in mathematical language. {3, 6,…

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Q: Consider the sequence x + 3, x + 7, 4x − 2, . . . . . . . . . . . . . (a) If the sequence is…

A: You have asked more than one different question. As per the guidelines we will solve first question…

Q: a Calculate the first 28 terms of the Diginacci sequence with starting terms 1 and 1, and then find…

A: We will answer the first question as we don't answer multiple question at a time. Please resubmit…

Q: a Calculate the first 28 terms of the Diginacci sequence with starting terms 1 and 1, and then find…

A: Given That:  In Diginacci sequence, First two terms  are less than 100 To Show  : c) It has a term…

Q: I. Determine whether or not each of the following is an arithmetic sequence.

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Q: Write an explicit formula that can be used to find the value of an, the n th term in the sequence.…

A: Given : a = first term = 512 common difference ==6-512=12

Q: Suppose that a sequence is defined as follows. a1=-5, a,=4a, +10 for n>2 List the first four terms…

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Q: Write down the first five terms of the following recursively defined sequence. a1 = 1; an+1 = – 2an…

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Q: Consider the following sequence: 3,9,15,21,... Find the 50th term of this sequence.

A: This is an arithmetic sequence with the common difference =d= 9-3=6 And the first term = a_1= 3

Q: Use the following information to answer the questions. The 6th term in the arithmetic sequence is 35…

A: It is given that, the 6th  term is a6=35 and 9th term is a9=50

Q: In an arithmetic sequence {a1, a2, az, · .....} the first term is 6 and the 20th term is 101, then…

A: Given : a = first term =6

Q: The following sequence is defined recursively, use iteration to guess an explicit formula for the…

A: The solution is given as

Q: Refer to the following arithmetic sequence: 2, 10, 18 , 26, 34, 42, .... What is a recursive formula…

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Q: Find as of the geometric sequence if a1 = 3 and r=7.

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Q: 1. What are the first five terms in the recursive sequence defined by the following? a1 = 150 an =…

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Q: Find an explicit formula for the general term  an  of the sequence. 1, −  1 3 ,   1 5 , −  1 7 ,…

A: We have to find the formula of general term.

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

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Q: Write down the first five terms of the following recursively defined sequence. a₁ = 3; an+1 = -2an…

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Q: Refer to the following arithmetic sequence: 2, 10, 18, 26, 34, 42, ... What is a non-recursive…

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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.