2. Find and prove a closed formula for the recursive sequence a, = 3, a, =a-2 %3D

Q: Find the 12th term of the geometric sequence 1, –4, 16, ...

A: Given  Geometric sequence   1,-4,16..... To do find the 12th term of the given sequence.

Q: Find a simple, closed form for the generating function of the sequence defined by a, n2. %3D

A:

Q: What is the closed form for the infinite geometric sequence beginning  4,2,1,1/2 where the first…

A: Given :The infinite geometric sequence : 4, 2, 1, 12, ..

Q: 1. Find the sum of the following infinite sequence: 40, 20, 10, …

A: A detailed solution is given below.

Q: Find an explicit formula for the general term an of the sequence. {1,- -/-/- 3 5

A:

Q: Write an explicit formula for an, the nth term of the sequence 8, –4, 2, ....

A:

Q: Find the correct recursive formula of the given sequence. 3, -2, -7, -12,

A:

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 nth term of the geometric sequence. 16, 8, 4, ...

A:

Q: Write the first four terms of the sequence defined by the recursion formula. a1 = 3 and an = an-1 -…

A:

Q: Find the sum of the finite geometric sequence. E(-3)" - (-3)" – 1 n-1

A:

Q: Create an explicit equation for the recursively-defined sequence below. **Optional table** to help…

A: t1=15,tn+1=3·tn So, n=0 gives t1=3·t0                   ⇒15=3·t0                   ⇒t0=153=5

Q: Find the generating function for the finite sequence 2, 2,2, 2, 2, 2.

A: Step 1: Consider the provided question, Given, the finite sequence 2, 2, 2, 2, 2, 2.

Q: Find the sum (to the nearest hundredth) of the first 17 terms of the sequence defined by the…

A:

Q: Find the first 4 terms of the recursively defined sequence. a1 =-3, an+1= an+9

A:

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

A: Given: Sequence: {-1, 1, -1, 1, -1……. } 1) It is an infinite geometric progression in which:…

Q: Find the closed-form of the generating function of the following infinite sequence: (2, 4, 8, 16,…

A:

Q: Find the first 4 terms of the recursively defined sequence. a1=4, a 2 = 5, an+1=an+ an-1

A:

Q: Which explicit formula describes the geometric sequence { 1 1 1 3' 9 27 ' 81 .. n-1 an=+(n- 1) ()…

A: The given sequence is: 13,19,127,181,... That is: 13,132,133,134,... So, the general form of the…

Q: Find an explicit formula for the general term an of the sequence. (1,-1/3,1/5,-1/7,...)

A:

Q: Find a closed form solution for the following recursive sequence: An :4an-1+5 for n > 1 with the…

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Q: Find a closed form solution for the following recursive sequence: An 3an-1+2 for n > 2 with the…

A:

Q: Find the first four terms of the sequence recursively defined by a1 =3 and an = n + 2an-1.

A: Given, first term of sequence is And terms of sequence recursively define by

Q: Find a formula an for the nth term of the arithmetic sequence whose first term is a1 = −6 such…

A:

Q: 1,0,

A: Given: The sequence is 0 , 1-e11+ e2 , 1- e21+ e3 , 1- e31+ e4  , 1- e41+ e5 , .  . .

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

A: Consider the given information a1=2, ak+1=3ak-5. Obtain the first five terms of the sequence as…

Q: Find the sum of the first five terms of geometric sequence. a1 = -5, r = 4

A: We know that, sum of n terms of an geometric series with first term a and common ration r is given…

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

A: Given,                a1=5,                       ak+1=7-2ak

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 first four terms and the 100th term of the sequence whose nth term is given. an =2n−4

A: To find the first 4 terms we will plug n=1,2,3,4 respectively

Q: Find the sum Sn of the arithmetic sequence that satisfies the stated conditions.

A:

Q: Create an explicit equation for the recursively-defined sequence below. **Optional table** to help…

A:

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

A: Given sequence is: ak+1=ak1k We have, a1=2 We have to find the first five terms in this sequence.

Q: 1) Write out the first three terms of the sequence explicity. 1+n n=0

A:

Q: Find the first 4 terms of the recursively defined sequence. a =3, a2 =4, an +1=an + an-1

A: Topic- recursive sequence A3 =7

Q: find the third fourth and fifth terms of the following recursive sequence

A: 11. The recursive sequence is An=2An-1-An-2, A1=4, A2=8. The third term is,…

Q: Please propose a formula for the elements of the following sequence a, which begins: 1, 3, 5, 7, .

A:

Q: 5. Find the 6th term of the recursive sequence defined by a₁ = 0, an+1=2a₁ +3.

A:

Q: Find the fourth term of the recursively defined sequence. 1 an = 5 2 + a n-1

A: To find the fourth term of the given recursively defined sequence.

Q: Find the formula of the general term an of the sequence:

A:

Q: Find an explicit formula for a sequence of the form  a1,  a2,  a3,     with the initial terms given…

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Q: Find the first four terms and the nth term of the infinite sequence defined recursively as follows:

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Q: Find an explicit formula for the sequence 1/2,-1/3,1/4,-1/6....

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Q: Find the sum to the nearest tenth of the first 17 terms of the sequence defined by the recursion a…

A: Given first term ( a ) = 5 Next term of series = 1.1 + an-1 This defines an A.P. with first term of…

Q: Give a recursive definition of the sequence {an}, n = 1, 2,... if: a. an=4n-2 b. an=1+ (-1)"

A:

Q: If the sequence 1, 0.3, 0.09, 0.027 is a geometric sequence, find the sum of the first five terms.

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Q: Find the first five terms of the sequence defined recursively below:   t1 = 2 tn = - 2t n-1 -2

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Q: What is the fourth partial sun for the geometric sequence a1=18 and r=2

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Q: Write an explicit formula for the geometric sequence  4.  – 4/3, 4/9, -4/27, …

A: Calculation are as follows

Q: Find the first four terms of the sequence with a recursive formula.

A: We have a recursive formula here. In a recursive formula, every subsequent term is derived from the…