The recursive formula to deseribe a sequence is shown below. aj = 3 ɑn = 1 + 2a-1 State the first four terms of this sequence. Can this sequence be represented using an explicit geometric formula? Justify your answer.

Q: Write the terms of a sequence defined by a recursive formula Question Given the sequence r, defined…

A: We find r2 by plugging n=2 and r1=2 in the formula for rn

Q: The first term of a sequence along with a recursion formula for the remaining terms is given below.…

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Q: write an expression for the apparent nth term (a„) of the sequence. (Assume that n begins with 1.)…

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Q: An arithmetic sequence is given below. 18, 14, 10, 6, Write an explicit formula for the n th term…

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Q: Write the terms of a sequence defined by a recursive formula with more than one initial term…

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Q: Un=11n-7  Calculate  the first 4 terms of the sequence

A: For the first term, n=1, so Un=11(1)-7=4For the second term, n=2, so Un=11(2)-7=15For the third…

Q: The first term of a sequence along with a recursion formula for the remaining terms is given below.…

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Q: Write the explicit formula for the nth term of the sequence below. 3, 2, ? 3' 3' 5 3 7 4

A: solve and observe the pattern that seuence follow.

Q: Write the explicit formula of the sequence 25, 21, 17, 13

A: Given 25,21,17,13 It is in arthematic series Because it has difference 4 for each number.

Q: The first term ao of a geometric sequence is -10, and the common ratio r is -3. What is the…

A: The formula for the nth term of a geometric sequence is given by an=a0rn-1, where a0 is the first…

Q: The first term of a sequence along with a recursion formula for the remaining terms is given below.…

A: Given, a1=1, an+1=-1n-1an2

Q: Write a recursive formula for an, the nth term of the sequence 17, 10, 3,.... An

A: In this question we are given with series and we have to find the first term and the general term…

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

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Q: The table below identifies the values for the first 5 terms in an arithmetic sequence. 1 2 3 4 Term…

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Q: An arithmetic sequence is given below. 18, 14, 10, 6, .. Write an explicit formula for the n th term…

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Q: The given pattern continues. Write down the nth term of the sequence {an} suggested by the pattern.…

A: Consider the given pattern. 4,-8, 12, -16,...  It is an alternating sequence having negative even…

Q: For Exercise, the nth term of a sequence is given. Write the first four terms of the sequence. d, =…

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Q: C. Using the recursive definition =3 (a,)` - ; if a, = 2. Create a sequence for the first five…

A: a1 =2 a2=7 a3=142

Q: Find the explicit formula for the given sequence. 2, 8, 32, 128, . .... a = 2.4"-1 A a = 8.4"-1 %3D…

A: We have the given sequence is 2,8,32,128............

Q: 3. Given the recursive sequence defined by a1= 1, az= 2, an= 3an-r+2an-2 , find the terms a3, a4,…

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Q: An arithmetic sequence is given below. 16, 20, 24, 28, Write an explicit formula for the n th term…

A: Given query is to find the explicit formula for nth term.

Q: An ontario lottery has the following structure,the first person drawn from the names wins $15000.…

A: We will find out the required values.

Q: The general term of a sequence is given and involves a factorial. Write the first four terms of the…

A: we have to write the first four terms of the given sequence whose general term is given as an=n2n!

Q: Write the terms of a sequence defined by a recursive formula Question Given the sequence t, defined…

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Q: In an arithmetic sequence a1, a2, , an, if the first term is 4 and the common difference is 4, then…

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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: The table below identifies the values for the first 5 terms in an arithmetic sequence. 1. Term…

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Q: Write a recursive formula for an, the nth term of the sequence 4, –16, 64, .... | An || ||

A: Question is solved.

Q: write the first five terms of the sequence. (assume Hhat begins with 1.) an= 5(-1)***() %3D

A: The objective is to write the first 5 terms of the given sequence.

Q: In an arithmetic sequence a1, a2,, an , if the first term is 6 and the common difference is 4, then…

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Q: 6. Consider the sequence defined by the recursive formula an = 10 - a,-1 with ao = 2 (a) What are…

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Q: Consider the following recursive sequence. Find the next four terms a2, 93, a4, and a5. a₁ = 2 a1 an…

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Q: What are the first 5 terms (starting with ao) of the sequence described below? an = 2an-1 - an-2…

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Q: Use the recursive definition to find the first four terms of the arithmetic sequence it defines. an…

A: To find the first four terms

Q: Show that the sequence is arithmetic. Find the common difference, and write out the first four…

A: Cn=6-8n when n=1 C1=6-8(1)=-2n=2C2=6-8(2)=-10n=3C3=6-8(3)=-18n=4C4=6-8(4)=-26 the sequence is…

Q: Write the terms of a sequence defined by a recursive formula with more than one initial term…

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Q: Write an expression for the apparent nth term (an) of the sequence. (Assume that n begins with 1.)…

A: This is a geometric sequence with a common ratio(r) : First-term is = a_1 = 1/3

Q: 1 The table below identifies the values for the first 5 terms in an arithmetic sequence. 1 2 3 4 5…

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Q: Given the explicit formula for an arithmetic sequence find the first five terms and the 52nd term:…

A: Given, an = -10n - 26 for 1st term n = 1 ,  a1 = -10 *1  - 26 = -36 for 2nd term n = 2 ,  a2 = -10…

Q: Use the formula for S, to find the sum of the first five terms of the geometric sequence. 5 5 15,…

A: Consider the sequence, 15,  -5,  53,  -59, ......................... The sum of the first “n” term…

Q: Write an explicit formula for the nth term of the arithmetic sequence. Find the sixth and tenth…

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Q: Given the following arithmetic sequence 3, 7, 11,. , find the value of the 17th term and the sum of…

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Q: write an expression for the apparent nth term (a„) of the sequence. (Assume that n begins with 1.)…

A: Consider the sequence 0,3,8,15,24.....................

Q: An arithmetic sequence is given below. 17, 14, 11, 8, ... Write an explicit formula for the n th…

A: We have to find

Q: In an arithmetic sequence a1, a2, · ·., an , if the first term is 3 and the common difference is 4,…

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Q: write an expression for the apparent nth term (a„) of the sequence. (Assume that n begins with 1.)…

A: By "the nth term" of a sequence we mean an expression that will allow us to calculate the term that…

Q: (a,) is a sequence and a, =3, n21 for 5a1=a. What is the general term of this %3D sequence?

A: see next step

Q: Write an expression for the apparent nth term (a,) of the sequence. (Assume that n begins with 1.)…

A: 91, 82, 73, 64, 55, ....... It is an arithmetic sequence with

Q: Write an explicit formula for a_nan​, the n^{\text{th}}nth term of the sequence 180, -30, 5,

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

A: a1=10 and an=an-1+2

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.