2. For the sequence 1, 5, 12, 22, 35, 51, ... i) Use subscript notation to write a recursive formula for the sequence. ii) Write an explicit rule to find the nth term.

Q: Determine whether sequence having the given nth term is monotonic           an = 3 + (−1)n

A: an = 3 + (−1)n We need to determine whether the sequence having the nth term is monotonic or not.

Q: Consider the infinite integer sequence 1, 3, 7, 15, 31, 63, ... Find a recursive definition for this…

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Q: If F, = 6 and F2 = 3, list the first 8 terms of this Fibonacci-type sequence.

A: topic - fibonacci type sequence in fibonacci sequence, The next number is found by adding up the two…

Q: Is the sequence {cos (-)- In(n)}, monotone? If so is it increasing creasing? or de-

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

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Q: Find the first five terms of the explicit arithmetic sequence. an = 4n 2 %3D O 2, 3, 4, 5, 6 O 6,…

A: we have to find the first five terms of the explicit arithmetic sequence an=4n-2 .

Q: Find a formula for the sequence of even numbers and a formula for the sequence of odd numbers.

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Q: A sequence can be generated by using an = 3a (n – 1), where a1 = 5 and n is a whole number greater…

A: Given,     an=3an-1,  where  a1=5 and n is whole number greater than 1.

Q: Show that the sequence 9,12,15,18, ... is an AP. Find its 16th term and the general term.

A: We need to show that the sequence 9, 12, 15, 18, ... is an AP. Here, 12 - 9 = 15 - 12 = 3. And the…

Q: For the set { 9 , 14 , 19 , 24 , .  .  .}   a)  ________________  is the general term for this…

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Q: Find the first five terms of the recursively defined infinite sequence.

A: Given that, ak+1=14aka1=128

Q: What are the initial term and a recursive formula for this sequence: 4, 7, 10, 13, ......

A: The given sequence is 4,7,10,13,... the common difference is 7-4=3,10-7=3,... therefore, the common…

Q: determine the closed formula that generates the sequence 1,2,4,8,16,32

A: The given sequence in the question is:

Q: Find the explicit formula for the given sequence. 2, 8, 32, 128, ....

A: TO find the explicit formula of given sequence .first check the common ratio terms since ratio is…

Q: Determine whether sequence having the given nth term is monotonic           bn = 2n /(1 + n)

A: Given sequence is bn=2n1+n A sequence is monotonic if it either increasing or decreasing through out…

Q: Find the first five terms of the recursively defined infinite sequence.a1 = 10, ak+1 = 1 + 1/ak

A: Given that, a1=10ak+1=1+1ak

Q: Find the first five terms of the recursively defined infinite sequence.

A: Given a1=5 ,ak+1=kak To  find the first five terms…

Q: Find the erplicit formula for the sequence 25, 5, 1, ,.

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Q: state the recursive formula that generates the last number in the sequence 1, 2, 3, 5, 7, 11, 15,…

A: The given sequence is 1, 2, 3, 5, 7, 11, 15, 23, 31.

Q: The sequence is defined using recursion formulas. Write the first four terms of the sequence.a1 = 4…

A: Given recursion formula, an=2an-1+3 for n≥2 a1=4

Q: Consider the sequence: 17, 14, 11, 8, ..., find the 26th term of the sequence.

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Q: In the sequence 4, 9, 14, 19, 24, 29,......n. Determine the recursive formula for the given sequence…

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Q: Suppose the sequence {an} is defined by the explicit formulaan = 1/n, for n = 1, 2, 3, ⋅ ⋅ ⋅. Write…

A: Given:an=1n, n=1,2,3.........a1=?a2=?a3=?a4=?a5=?

Q: Find the first five terms of the recursively defined infinite sequence.a1 = 9, ak+1 = √ak

A: Given: The recursively infinite sequence in which a1=9, ak+1=ak. To find the first five terms of the…

Q: The sequence is defined using recursion formulas. Write the first four terms of the sequence.a1 = 2…

A: a1=2 , an=5an-1

Q: The sequence is defined using recursion formula. Write the first four terms of the sequence: a1 = 4…

A: The first term is a1 = 4  and an = 2an-1 + 3 for n ≥ 2

Q: (2) Identify the next likely term in the sequence and the type of sequence: 5000, 2000, 800, 320,…

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Q: 9. Find the explicit formula for a sequence satisfying а, %3D10а,, + 25а, _,n22 n-1 а, %3D 3, а,…

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Q: A sequence is defined recursively as below: di = 3dr-1+4, for all integers k > 2 and di = 3 Guess an…

A: First we'll find its characteristic equation and then find the roots of the characteristic equation

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: Determine if the sequence is a geometric sequence. If it is, find the common ratio and write the…

A: Given: A sequence: 294,42, 6,6/7,.................................. To find: If sequence is…

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

A: .

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: the n^th term of the following sequence 1,4,7,10,...is

A: For given sequence a1 = 1 a2= 4 a2 = a1 + 3

Q: The sequence is defined using recursion formulas. Write the first four terms of the sequence.a1 = 5…

A: Given that, an=3an-1-1a1=5

Q: Find the first 4 terms and the eighth term of the recursively defined sequence. C1 = 7, c2 = - 2,…

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Q: Find the first five terms of the recursively defined infinite sequence.

A: a1=2 , ak+1=akk

Q: Let the arithmetic sequence be defined by the formula un=11+(n - 1) x 6 Apply the concepts of the…

A: An arithmetic sequence is a set of numbers that obey a specific mathematical expression called its…

Q: Consider the sequence: 2, 4, 8, 16, 32, ...Determine the 13th term of the sequence.

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Q: Find a closed formula for the sequence defined recursively by bo = 2, by = 3 and b, = 3b,-1 – 2b,-2…

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Q: 35. Prove that the sequence {n!}^, beats the sequence {2"}-1-

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Q: Provide a simple formula or rule that generates the terms of an integer sequence 2, 16, 54, 128,…

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Q: Show that if a and x are any two nonzero real numbers, then ,-1,,-.. is a geometric sequence.

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Q: Which recursive rule describes the sequence 3, 7, 11, 15, ... ?

A: First we have to find out 1st term and common difference.

Q: The sequence is defined using recursion formulas. Write the first four terms of the sequence.a1 = 3…

A: a1=3 , an=4 an-1

Q: Find a formula for thr nth term of the arithmetic sequence. 24,22,20,18,16, …

A: Given query is to find the nth term of the sequence.