Consider the sequence {n} defined by ₁ = = 3.1, T₂ = 3.14, T3 = 3.141,...; for each n, πn shows the first n decimal digits of 7. Show that {n} is a Cauchy sequence.

Q: 8. Give the first five terms of the following recursively defined sequence: a1 = 2. and ar = ax-1 +…

A: Recursive definition of a sequence is one in which one term can be determined using previous terms…

Q: Find the 11th term of the harmonic sequence1/5,1/8/1/11,1/14,. . .

A: harmonic progression is 1arithmetic progression the given series has a pattern of = 13+previous term…

Q: 25. Write the nth term of the sequence 2, 8/3, 32/9, 128/27... as a function of n.

A: Given,          2,  83, 329. 12827, . .  .

Q: Find a FORMULA for the general term an of the sequence {12, 4, −4, −12, −20, } assuming that the…

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Q: The sum of the first 20 terms of the sequence 0.7, 0.77, 0.777, ... is

A: The given sequence is 0.7,0.77,0.777,...... The sum geometric sequence with common ratio r<1 ,of…

Q: Find the sum of the first eight terms of the sequence 1/8,−1/4 ,1/2 ,.... please show working

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Q: sequence: Find an explicit sequence formula that will generate the following 8, 9, 11, 15, 23, ...

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Q: Find the seventh term and the sum of the first seven terms of the geometric sequence 6, −3,32, −34,…

A: Given: A geometric sequence is given.6, -3, 32, -34, ... To Find: The seventh term and the sum of…

Q: Suppose that g1, 92,93, ... is a sequence defined as follows: 91 = 3, 92 = 5, gk = 3gk-1 - 2gk-2 for…

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Q: Assume "t*1*" represents the first term of a sequence and "t*n*" represents the nth term. What is…

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Q: Find n such that the geometric sequence becomes less than 1: {400, 240, 144, 86.4, ...} n3D

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Q: Indicate the generating function of the sequence defined by ak = = 4ak-1 +5

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Q: 4. Find the value of x so that x+7, -x-1, x+ 13,.. shall form a geometric sequence.

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Q: One of the following sequence is convergent: Select one: O a. None of these Ob(-1)**'v2n} 2n O…

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