1 na sequence, the first term is 4 and the common difference is 3. What is the fifth term of this equence? 1) –11 2) 16 3) 19 4) -8

Q: 79. In Exercise 103 from Section 11.3, we learned that if a fair coin is flipped n times, the number…

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Q: In a geometric sequence t, = 625, and the common ratio is r = For what value of 1s t %3D 25

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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: 4.) Consider the arithmetic sequence 23,34, 45, 56 .. a.) Find the 25th term of the sequence. b.) Is…

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Q: In the Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, ...}, what is the value of Fg ? D F = 21 OF = 34 D F…

A: Given : Fibonacci Sequence 0,1,1,2,3,5,8,..To find :F8

Q: Find the common ratio and write out the first four terms of 7n+2 the geometric sequence 6 Common…

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Q: 1. Make a conjecture given that AABC is an equilateral triangle. 2. Given: ZA and ZB are…

A: 1. Given that △ABC is an equilateral triangle. Conjecture:  All the sides are equal, AB = BC = CA.…

Q: 4. There is a stack of logs in the backyard. 15 logs are in the first layer; 14, in the second; 13,…

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Q: 9. A sequence is defined by the rule a, = +n with a, = 20. Find the value of a, %3D

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Q: 1 The sequence an %3D 2n +3 (a)decresing (b) in

A: See the details solution in below

Q: the 3 terms Of an arith metic sequence are 3K+1, SK, 6K+9 a) show that K=5 b) Find the values of the…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Let Fib(n) be the nth term of the Fibonacci sequence, with Fib(1)=1, Fib(2)=1, Fib(3)=2, and so on.…

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Q: 9. a) The formula for the nth term of the sequence n(n+1)(2n+1) 1, 5, 14, 30, 55, 91,... is 6 Find…

A: Given that:(a) 1,5,14,30,55,..  nth term = n(n+1)(2n+1)6(b)10, 17, 26, 37, 50,..., nth term…

Q: A sequence ao, a1, a2, .. .satisfies an = n an-1+(-1)" for n > 1. If a5 = 44, then az %3D

A: Since, a sequence a0,a1,a2,..... satisfies an=n.an-1+(-1)n-(i) for n≥1.Ifa5=44. Our Aim is to find…

Q: parent, but a male bee has only a female parent. There- fore, the number of ancestors of a male bee…

A: Given: 1,2,3,5,8,13 To write the 3 more terms of the Fibonacci sequence. Fibonacci  Sequence: The…

Q: Which of the following statements is true about Fibonacci sequence and the Golden ratio? O a. The…

A: We know that, Golden ratio=limn→∞Fn+1Fn

Q: 8. Given the geometric sequence: 2, 32 11' 121 Find an explicit formula for an- Find az = %3D

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Q: 12. What is the next term in the Fibonacci sequence 1, 1, 2, 3, 5, 8 ...? а. 11 b. 12 С. 13 d. 14

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Q: 3. Consider the pattern manifested by the tiles below. az az a4 as (a) What is the nth-term formula…

A: To find first five terms of the sequence,we substitute n=1,2,3,4,5 in the expression of Tn. After…

Q: 14. In a sequence of three squares, the second and third squares are symmetrically in- scribed…

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Q: II. Answer the following: 1. Calculate for the perimeter and area of a regular 13-gon of side length…

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Q: An 9-gon fractal pattern has the sequence {1, 9, 81, 729, ...}. The recursive formula is az = 1,a, =…

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Q: A recursive formula for the sequence 18, 9, 4.5, ... is 1 91 = 18; gn = = In-1 1. 9n = 18( -1 2. 91…

A: Given- g1=18,gn=12gn-1 Putting n=2, g2=12g1=12×18=9 Putting n=3, g3=12g1=4.5 According to this…

Q: Is the sequence an :4n – 19 arithmetic? Your answer is (input yes or no) if your answer is yes, its…

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Q: 1. determine the nth term formula for the number of square tiles in the nth term figure. 2. how…

A: Given number of square tiles in first, second, third, fourth and fifth figure are 5, 8, 11, 14, 17…

Q: iven the pattern 12,6,0... Determine the formula for the n(the) term in the sequen

A: To determine the formula for the nth term for the below sequence. 12, 6, 0, ....

Q: Consider the sequence given by an = 2 – 6n. a. Find the first 6 terms of the sequence. What sort of…

A: Solutions:-4

Q: 1. Given the sequence:25, 21, 17, 13,..Write the explicit equation that models the sequence. O a) an…

A: Given: 25,21,17,13

Q: 2" An 2n+1

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Q: 3. In a geometric sequence, if az = -5 and ag = 40, determine a1, r, and an. Then write the first…

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Q: An octagonal fractal pattern has the sequence {1, 8, 64, 512, ...}. The recursive formula is a, =…

A: The given sequence is 1,8,64,512,..... We have to find the recursive formula of the above-given…

Q: Given 1. In the sequence 0 ,-5, -10, -15, what is the 3rd term? 2. If az = -3, d= 4, what is the 1*…

A: AP

Q: In geometric sequence a1, a2, - --, an , if a4 = 1472 and a6 23552, then the common ratio is O 4 O 5…

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Q: let be a sequence sit. 2 for oxaza2 12 then 6'mam=? 348

A: Let an be a sequence  such that for 0<a1<a2 an+1=an+an-12,n⩾2. Find limn→∞an.

Q: As which term does appear in the sequence 81, 27,9...? a. 5th b. 11th 8th с. d. 15th е. 12th

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Q: B. Use inductive reasoning to predict the next three items in each list. Make a conjecture for the…

A: B) 1. The given sequence is 1, 3, 6, 10, 15, . . .This sequence follows the pattern as +2, +3, +4,…

Q: 12. Which of the following represents the formula of Fibonacci sequence.

A: The next term in the Fibonacci sequence is find out by adding previous two numbers of the sequence.

Q: The following pattern is established involving terms of the Fibonacci sequence. Use inductive…

A: Introduction: Every number in the Fibonacci series, often known as the "Fibonacci numbers," is the…

Q: if the pattern continues, what will be the next term in te sequence 4, 1, -2, -5?

A: Given4,1,-2,-5

Q: 9. Two recursive sequences u, and v, are defined by 1 Uo = 9, Un+1 =5Un – 3 2 Vn = Un + 6 i) Show…

A: We’ll answer the first three subparts of the question since the exact one wasn’t specified. Please…

Q: Suppose the sequence is 1 2 3 4 5. 6. 2 5 10'17' 26'37 6. Then a formula for the n-th term is an =…

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Q: In geometric sequence a1, a2, · ·… · , an , if az = 686 and ag = 33614, then the common ratio is O…

A: Given a1,a2,a3…,an is geometric sequence.  To find the common ratio if a3=686 and a5=33614.…

Q: In geometric sequence a1, a2, · -, an , if az = 416 and a5 6656, then the common ratio is O 64 O 4 O…

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Q: 16. (a) Fill in the blanks to continue this dot sequence in the most likely way. 1 , 2 (b) What…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: An octagonal fractal pattern has the sequence (1, 8, 64, 512, .). The recursive formula is az = 1,a,…

A: Option C  is true.

Q: 6. Write down the first 8 terms of the Fibonacci sequence and if F, is the nth F. for n = 7, 8, 9. .…

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Q: A test question lists the first four terms of a sequence as 2, 4, 6, and 8 and asks for the fifth…

A: Given sequence is: 2,4,6,8, Here we observe that: 4-2=26-4=28-6=2 Thus, we observe that each…

Q: The fourth term of a geometric sequence is 135 3645 and the seventh term is 4. Find the first 32…

A: Given :                     The fourth term of the geometric sequence is 1354 and seventhterm of…

Q: In each case, find the first 5 terms of the sum and compute S. er: The first 5 terms are: The sum is…

A: Solving by geometric progressions we have

Q: a) The number pattern 1; 6; 19; 40 ; ... is represented below. Calculate Tn and then the 17th value…

A: Number pattern 1,6,19,40....For above pattern  the patttern we find is tn=4n2-7n+4put n=1 we get…

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.