1. What are the next three terms of the sequence shown below? 3,–6, 12, –24, .. 2. Evaluate: 4 3 Σ -5) x =2 3. Evaluate: 4 E 2k-1 k = 1

Q: The general term of the sequence is 2 -1 2 -1 2. - 1층글룸금.... 25 3 an = (-1)"+¹ ²1, n ≥ 1 (−1)²+12 n

A: Given :an=-1n+12n

Q: Find the first three terms of the sequence whose nth term is given. Sn = 3n - 2 A51=1, 52 = 2, 53 =…

A: Given : sn = 3n - 2

Q: 4. What is the 11th term of the geometric sequence {1,000,000; 100,000; 10,000; ...}? O a11 = 0.100…

A: Here we find the 11th term in geometric sequence.

Q: All changes saw 12. Find the first 5 terms of the sequence where a1 8 and an = an-1+7 where n > 1.…

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Q: What is the first term of the geometric sequence presented in the table below? 3 8. 84 -2,688 Hint:…

A: topic - geometric progression

Q: 16.Consider the first 3 terms of the sequence a, (where k 2 2). A. Give the first 3 terms of the…

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Q: d.Write only the first 4 terms in the sequence defined by the formula given below: k az = 2 for all…

A: First four value is  0 ,0 ,2 ,2

Q: 1. Consider a sequence that begins with 1, 4, 8, Explain why each of the following could be the next…

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Q: (a) A town has a population of 5000 persons, but is expected to grow by 2% every yea (1) What would…

A: Given, Initial population of a town is 5000 persons. It is given that it increases at a rate of 2%…

Q: 00 Write the first four terms of the sequence (an} n=1 n+1 3n - 1 3 1 5 О А. 1, 5' 2' 11 3 1 О В. -…

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Q: 19 Find the explicit formula for the given sequence. 2, 8, 32, 128, .. A an = 2+4 (n – 1) B an = 4+2…

A: Given sequence 2,8,32,128...... We notice that  a1=2=21 a2=8=23 a3=32=25 .......

Q: 1. What is the 5th term of the geometric sequence described by a, = 5(1.5)"? %3D O az = 5.0625 %3D O…

A: The given question can be solved as shown in step2

Q: > The general term of the sequence 1,!! ! , starting by n-0 is (6) 2n+1 (ii) (iii)None of these

A:

Q: Which of the following represents the Fibonacci sequence? O a1 = 1, a2 = 1, an = an-1 – an-2, for…

A: We will find the Fibonacci sequence.

Q: S) Predict the nth term of the sequence, given the first five terms. a1 = 2, az = 5, az = 10, a4 =…

A: Given: first 5 terms area1=2; a2=5; a3=10; a4=17; a5=26

Q: 3. What is the 10th term of the sequence whose nth term is an = (n^2+2n-3)/(n+1) ? * O 117/11 O…

A: We are given the nth term of the sequence and we need to find the tenth term of the same. This can…

Q: 14. Which explicit formula describes the geometric sequence {, ,7 8T}? 1 1 O an = (3)"-1 O + (n –…

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Q: 1. Find the 10th term of the arithmetic sequence in which aj = 12 andd = 9.1. O a10 = 103.9 O a10 =…

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Q: 03. What is the third term of a sequence given the explicit formula? аn 3 —5 + 2(п — 1) А. -5 В. -3…

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Q: Find an explicit formula for a sequence of the form a,, az, a3 with the initial terms given below.…

A: To find  An explicit formula for a sequence of the form with the given initial terms.

Q: The repeating decimal 0.555 can be represented as the sum of a geometric sequence where a is the…

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Q: 1. Give the first five terms of the sequence with the given general term. a. a, = 3n+4 %3D b. а,…

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Q: Find the nth term of the given sequence, where n= 1,2,3... 1/5, 4/9, 9/13, 16/17...

A: The given sequence is 15, 49, 913, 1617,⋯ Here numerators of the fractions are 1, 4, 9, 16 which are…

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: The following sequence is geometric: -1, 1, -, . O True O False

A: Given the geometric sequence−1,12,14,−18

Q: 4. Find Sn for the following geometric sequences described. a. aj = 16, r =, and n = 7 b. ai = 4, an…

A: For a GP series a, ar, ar2, ............. where a = first term             r = common ratio…

Q: Let (an) be the sequence defined by a1 = 5 and an = 2an-1 – 3 when n > 2. What is a4?

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Q: Given that the first term of an geometric sequence is 2 and the common ratio is 3 what is the…

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Q: Which is (are) the initial condition(s) for the Fibonacci sequence? O F, = 1, F1 = 1 O F, = 0, F1 =…

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Q: 1. Which of the following represents an explicit formula for a given sequence? 1. A(n) = 2 A(n – 1)…

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Q: Find a fomula for an given the few terms of the sequence. 1/2 , 1/4 , 1/8 , 1/16 , ....

A: We can solve the problem by obtaining the nth term of the sequence.

Q: write an expression for the apparent nth term (an) of the sequence and assume that n begins with 1…

A: The sequence is given by 31, 42, 53, 64,75,····· To evaluate : The expression for the apparent nth…

Q: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

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Q: Find the first 5 terms of the following sequences and then write the sequence in list form. a) Let…

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Q: 6. Write an nth term (general term) of the geometric sequence that has the given two terms: a. t, =…

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Q: Determine the first four terms of the arithmetic sequence represented by the explicit formula an =…

A: Given, an=7(n-1)+8Here we consider n>0

Q: 5. Write down the first five terms of the sequence given by (-1)"+1 an = Determine the following.

A: Since we are given with the multiple number of question and answered according to the guideline.

Q: 1. Consider the sequence defined by the explicit formula AN = N² +1. a) Find A₁ = b) Find A100 = c)…

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Q: Which of the following are geometric sequences? Select all correct answers. Select all that apply:…

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Q: The general term for the sequence , . is: 3n n+1 3n 3+2 n+3 n+1

A: Given:     To determine: The general term of the given sequence.

Q: Given the arithmetic sequence of 4, 2, 0, -2, . .fund an explicit rule for the nth term. O an = an 1…

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Q: For the sequence defined by s, = E(? – i), complete the first three rows of the difference table i=1…

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Q: 17. What is the first 5 terms of the sequence? Assume that n begins with 1. 1. an = 10 (-)" [A] 10,…

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Q: If the explicit nth term formula for the given sequence is an = 2n2 + bn +c, then b= and c= 5, 10,…

A: Plugging n=1, an=2n2+bn+ca1=212+b1+c5=2+b+cb+c=3 Plugging n=2, an=2n2+bn+ca2=222+b2+c10=8+2b+c2b+c=2

Q: 1 2 Which of the following formula is the general term of the sequence - 28 65 a. n+1 b. (2+1) O c.…

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Q: The nth term of a sequence is given. Find the first 4 terms. 2n 1 %3D + 2n 5 7 3 1, OT8 15'8 7. 1 1…

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Q: 7. Find the first five terms of the sequence defined by each of these recurre a) an = 6an-1, a0 = 2…

A: Introduction: A recurrence relation is a formula that describes a series based on a rule that…

Q: 2. Which is (are) the initial condition(s) for the Fibonacci sequence? Fo=1, F₁ = 1 Fo=1 F₁ = 0…

A: We can solve this as follows:

Q: Find the n th term a of a sequence whose first four terms are given. 5 6. 7 8 - ... 11 22 33 44'

A:

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.