a) Show that the sequence a, = (-1)" +- does not converge. b) Let b, be a sequence such that for all n we have bn+1-b,|< Show that b, is a Cauchy sequence.

Q: A is a sequence with the ratio between two consecutive terms constant. O arithmetic sequence O none…

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Q: Tell if each sequence is arithmetic, geometric or neither. Explain your choice. Determine the next 3…

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Q: Use any method to prove that if X = (xn) is a Cauchy sequence of real numbers, then () is also a…

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Q: (b) Let AB be the Dedekind cut for 30. Which of the following numbers are in A? 1, √2, 2,5/2, 7/2,…

A: Definition of Dedekind cut: A dedekind cut is defined as a partition of rationals into two subsets…

Q: An explicit definition for a sequence use the index of the term to define the value. O True O False…

A: An explicit definition for a sequence use the index of the term  to define the value Yes it is true.…

Q: 1 and LEFT LEFT USE A LEFT Approximate the area under the curve f(x) = -0.3x² + 20 between x = x = 5…

A: As per the question we are given the following function : f(x) = 0.3x2 + 20 Now we have to…

Q: Which of the following is the rule for the sequence 6, -6, 6, -6…

A: Given data: The given sequence is 6, -6, 6, -6..... The standard expression for the sequence is, a1,…

Q: a(Cick to select) For the sequence an= (n+1 the values of the first four terms of the sequence are…

A: an = (n+1)(n+1) a0 = 1a1 = 22

Q: sequence a1, A2, A3, 2 2 - 2 + ... an 2 ... 2 is an A.P., th n 102 =

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Q: Topic: Arithmetic Sequence 1.  a1 = 1 d = -5 a36 = ? 2.  3a + b, 5a + 2b, 7a + 3b, 9a + 4b,…

A: Given:- a1 = 1 ,d = -5   Find a36          2.      3a + b, 5a + 2b, 7a + 3b, 9a + 4b, ... To…

Q: ACTIVITY 3 Arithmetic Sequence I. Find the next three terms in each sequence. 1. 18, 11, 4, ... 2.…

A: topic- arithmetic sequence

Q: Write the next three terms of the sequence O, T,T,F,F,S, S, .... Your answer Write the next three…

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Q: The type of the sequence -10, -13, -16, -19, …. Is?   1.  None of the answers   2.  HP   3.…

A: Given sequence 10, -13, -16, -19, ….

Q: Geometric Sequences as Exponential Functions Homework For the following sequences, write each one in…

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Q: If these sequences continue, then which is greater, A(9) or B(9)? Explain or show how you know.…

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Q: Find the 60th term of the sequence 5, -2,-9,-16,... O a-478 O b.non of them

A: Here given as 5, -2, -9, -16, ...... The first term of sequence is a1=5, Also the common difference…

Q: Write a formula for the general term (the nth term) of the arithmetic sequence a₁, a2, a3, a4, ....…

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Q: Given a term and the common difference of an arithmetic sequences, find the explicit equation. a1 =…

A: Given that:a1=5 and d=12

Q: 7. Solve. (a) Find a recursive formula for the sequence 5, 11, 18, 26,35,45,... (b) Find a closed…

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Q: 3,-5,-13,-21 the sequence

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Q: Find the next two terms in this sequence. 800, 400, 200, 100, [ ? ], [ ]

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Q: A partial sum of an arithmetic sequence is given. Find the sum. 3+8 + 13+. . . +538

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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.