1. Find a formula for the nth term of the given sequence: 1,-1,1,-1,1,-1,... 2. What is the 1000th term of the following arithmetic sequence? 0,?,2?,3?,... 3. The eighth term of an arithmetic sequence is 33 and the 13th term is 19. Find the 20th term. 4. Which term of the arithmetic sequence 7,12,17,... is 352? 5.How many terms of the arithmetic sequence 3,5,7... must be added together to get 899? 6. The first term of a geometric sequence is 12, and the third term is 16/3. Find the fifth term. (Assume the ratio is positive) 7. Find the partial sum of the following geometric sequence. 2/3+1+3/2+...+27/8 8. Find the infinite geometric sum. 100+1+1/100+...

Q: 1. Write the first five terms of the sequence defined by i) a, = (-1)"+1 Li. ii) b, = . 2. Find a…

A: Given: Question 1(i)  an=(−1)n+11+nn!(ii)  bn=2nn!find five termsQuestion 2(i)…

Q: Determine the common ratio r, the fifth term, and the nth term of the geometric sequence. 1, 5, 5,…

A: G. P. Series problem.....

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: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

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Q: 5. Which geometric sequence has a first term equal to 55 and a common ratio of -5? O {55; 275;…

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Q: c) Write the explicit formula for the nth term of the sequence below. 5 3 3, 2, 2' 5' 3 7 4 ....

A: Explicit formula for sequence problem.....

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) The nth term of a sequence is Un. The sequen

A: Introduction: 1: the sequence in which things are or should be linked, related, or dated Follow the…

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: 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: 3. Which of the following is a geometric sequence O 30, 15, 0, -15,.. O 3, 9, 27, 81,..

A: Option b is only in gp

Q: Determine the common ratio r, the fifth term, and the nth term of the geometric sequence. 2, 2° + 1,…

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Q: If the first term of a geometric sequence is 3/2 and the second and third terms are -3/4 and 3/8.…

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Q: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

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Q: What is the recursive formula for the geometric sequence 2, 6, 18,54, O A an 3, if n = 1 3- a, if n…

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Q: 4 Which of the following sets represent an arithmetic sequence? A{-5, - 2, 1, 4, 7,...} B {2, 5, 9,…

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Q: Find the formula (nth term) of the sequence 7, 10, 15, 22, 31, .. . O an = (-2)" O an = (n-5)/4 an =…

A: As per company's guidelines, we are supposed to solve first question for you, kindly repost other…

Q: Find a formula for the nth term of the given geometric sequence. 7, 28, 112,

A: Given: 7,  28,  112,  ...

Q: 27 3. What is the formula for the nth term of the sequence: 8,-6, , 8. ...

A: The given sequence is 8, -6, 92, -278

Q: 1. Find the first five terms of the geometric sequence for which a1 3 and r = -2. %3D

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Q: Find the formula of the general term an of the sequence: 3 1 2 .. 1, 2 2

A: The solution is given as

Q: This list shows the first four terms of a geometric sequence. 4, 2, 1, 3,... Which function can be…

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Q: Consider the geometric sequence defined by an=3 (2) n–1 1. Find the first four terms of the…

A: The given geometric sequence is: an=3×2n-1

Q: 3. Given the recursive sequence defined by a1= 1, az= 2, an= 3an-r+2an-2 , find the terms a3, a4,…

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Q: A. Find the formula for the nth term of the following geometric sequence: 1/4, 2/4, 4/4, 8/4 B. If…

A: A.Given 1/4,2/4,4/4,8/4 Here a1=1/4 , r=(2/4)/(1/4)=2 an=a*r(n-1) an=(1/4)*(2/4)n-1…

Q: If the general term of an arithmetic sequence is a(n) = 7n - 3, find the sum of the first 7 terms of…

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Q: If {8,11, 14, 17,.....} is the given arithmetic sequence, then the common difference d = O 3 -8 -3 O…

A: The given sequence is                                 {8,11,14,17,.....}     The first term of the…

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: 3. Find a formula for nth term of the sequence 1, 1 1 4' 16' 25

A: Simplification

Q: Suppose that the 8th term of an arithmetic sequence is -1 and the 20th term is 2. Write the general…

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Q: 2. The sequence given by a, = ar" is a geometric sequence in which a is the first term and r is the…

A: The sequence given by an=arn-1 is a geometric sequence in which a is the first term and r is the…

Q: 5. The third term of an arithmetic sequence is 28, while the fourth term is 41. Write the sum of the…

A: Given:  Third term of arithmetic sequence =28                fourth term     =41  To find : Sum of…

Q: Given that the first term of an geometric sequence is 2 and the common ratio is 3 what is the…

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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: Find the missing term in each of the arithmetic sequence.. 1. 5, 15, , 25 4.49, 42, 28 1 2. -1,-5, ,…

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Q: If the first 5 terms of a geometric sequence are {12, 6, 3, the formula for the nth term in the…

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Q: 1 n(n+1)

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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: 10. Find the sum of the first 40 terms of the arithmetic sequence {1,6, 11, 16, . ..}. Make sure to…

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Q: Given a geometric sequence whose first term is 3 and its common ratio is Find i) the 8 term, ii) the…

A: a=3  &  r=12. i. Eighth term is, T8=ar7    ∵Tn=arn-1=3127=3128

Q: Given the arithmetic sequence of 4, 2, 0, -2, . .fund an explicit rule for the nth term. O an = an 1…

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Q: 12. The 8th term of an arithmetic sequence is 16, and the 18th term is 56. Find the sum of the first…

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Q: The general term of a sequence is given an = -2(n - 1)! and involves a factorial. Write the first…

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Q: Find the indicated term of the geometric sequence. 6th term of 3, 3/4, 3/16…

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Q: Write the first five terms of the sequence given by an = 2 ^n/n!, Begin with n=0

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: a) Suppose the fifth term of an arithmetic sequence is 18 and the sum of the first eleven terms is…

A: We need to solve these questions using the equations related to arithmetic and geometric sequence.

Q: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

A: Solving the problem by finding the n th term of the given sequence.

Q: What is the common ratio, a1, a2, a3, and a4 of this geometric sequence: {(7^(n-2))/3}

A: Consider the provided geometric sequence,

Q: B. Find the nth term of the sequence, then find the 2oth term. 5. 5. -6, -4,-2,..

A: Solution..

Q: <th For a given arithmetic sequence, the 6 term, a, is equal to 26, and the 35 term, azs, is equal…

A: Let a be first term of A.P.  And, d be the common difference, then

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.