Define the following sequence recursively, giving two instructions in mathematical language. {1, 4, 16, 64, ..} a1 = 1, a, = an-1'4, forn 2 2 a a1 = 1, a, = an-1 3, for n 2 2 a1 = 1, a, = an-1'4, for n < 2 d a1 = 1, a, = an-1 3, forn < 2

Q: The 2 – tail of the sequence Y = (1, 3, 5, 7, 9,... , 2n – 1, . ..) is: O Y = (7,9,..., 2n + 5, ...)…

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Q: Find two different explicit formulas for the sequence {1, -2, 3, -4, -5, ⋅ ⋅ ⋅}.

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Q: Find the generating function for the sequence 1,−2,4,−8,16,….

A: The general expansion of the binomial (1-x)-1 will be, (1-x)-1=1+x+x2+x3+….

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: Find an explicit formula for a sequence of the form a, a, a, 4, 8, 16, 32, 64, 128, 256 I an = with…

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Q: (1 point) Find a formula for the general term a, of the arithmetic sequence (starting with a1): {4,…

A: a1=4 a2=-2 a3=-8 a4=-11 Note that commond difference d=-6

Q: Write an explicit formula that represents the sequence defined by the following recursive formula:…

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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&lt;1 ,of…

Q: a = (k + 1)a, +1 and a =-1 [3] Let be a sequence defined recursively as , find a,, "3, and a..

A: I am attaching image so that you understand each and every step.

Q: Write down the first five terms of the sequence an a₁ = 92 = a3 = 04 = a5 = (n+2)! 2n

A: The given sequence is; an=(n+2)!/2nFind next five terms.

Q: erms a1, a2, 43,., IS deni an = 2", for n 2 1. The sequence B, with terms b1, b2, b3, .., is defined…

A: Given :-  The sequence A , with terms a1 , a2 , a3 , ..... are defined by  an = 2n for n ≥ 1. The…

Q: Which sequence could be described by the first term: Aj = 1 and the recursive (an)² + 1 definition:…

A: Given, an+1=an2+1 a1=1

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: Write an explicit formula for the sequence: 6 - 1' 7- T 8 9 - x 10 - * 7' 12 + 1' 18 + 12' 24 + ' 30…

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Q: A sequence has a recursive formulatn = tn-1+nº, tị = 5. Determine t3.

A: The given recursive formula of the sequence is: tn=tn-1+n3...(1) And t1=5

Q: Write down the first five terms of the following recursively defined sequence. a1 3; an+1 = an +9

A: It is given that a1=3;an+1=an+9.

Q: 12. Find the first 5 terms of the sequence: 2n a, =(-1)" n +1 a) b) a, = 4a-5 and aj =1 | n-1

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Q: sequences, in the form t(n) = a(b)" b) 3, -18, 108, –648, .. equation

A: We will look each term closely to find the explicit equation for the sequence.

Q: 1. For each of the following sequences, write down the first 4 terms of the sequence (an). (a) (급),…

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Q: Find the first five terms of the sequence defined by the following recursive definition. a, = 13 an…

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Q: The sequence n0.1 converges if

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Q: For the sequence {an} defined recursively by a₁ = 1, a2 = 1, An+2 an+2 +an+1 for n > 2 Write a 44

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Q: Give the first six terms of the following sequences. You can assume that the start with an index of…

A: Increasing sequence : If an is any sequence and an≤an+1 for all n .Then an is called to be…