10. Is there a pair of integers (a, b) such that a, x1, Y1,b is part of an arithmetic sequences and a, x2, Y2, b is part of a geometric sequence with x1, x2, Y1, Y2 all integers?

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

A:

Q: Suppose that n > 5 and that the numbers t1, t2, t3, . . . , tn−2, tn−1, tn form an arithmetic…

A: We need to determine the value of n in the given arithmetic sequence.

Q: For the sequence defined by: ai = 3 1 + 4 An ап +1

A:

Q: 1. Arrange the integers 1,2,3, . . . ,17 so that the sum of consecutive numbers is equal to a…

A: To find:  Arrangement of the integers 1,2,3, . . . ,17 so that the sum of consecutive numbers is…

Q: The following infinite sequence will be defined as recurrent relation: 1,10,3,20,9,30,27,40, ... The…

A: This question is related to sequences. The solution to the given question is explained below.

Q: Find an a and y such that 3, x, y, 42, ... becomes an arithmetic sequence. (Hint: and y should be…

A: We need to find x and y such that 3,x,y,42 are in Arithmetic sequence and x and y such that…

Q: 2)Define the sequence: a, = (n+1)! (n = 1,2,3, ...) recursively. %3D

A: Given  an = (n+1)!

Q: Suppose that the sequence {ax}1 is 2, 4, 6, 8, 10, 12, 14, 16, ... What is a4?

A: Answer

Q: 1. Here are the first two terms of some different arithmetic sequences: -2, 4 11, 111 5, 7.5 5, -4…

A:

Q: 4. Give a recursive definition of the sequence an if an = n(n+1), where n = 1, 2, 3, ... %3D

A: We have to give a recursive definition of the sequence an where an=  n(n+1) for n= 1,2,3,....

Q: Terms of the sequence a1, a2, a3, ·.., a2020 are obtained by the rule: 1+ a2 1+ a2019 1+ a1 1- a1 az…

A:

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: explicity. 3) Write out the first three terms of the sequence 3+2n

A:

Q: The figure below shows the first three squares in a sequence qo, 41, 42, - - . of squares divided…

A:

Q: Determine the pattern and find the missing terms in each of the following sequences. 1. 2, 5, 10,…

A: A) 1.   This sequence  has terms  which are incremented by odd numbers starting  from…

Q: Suppose that g1, 92,93, ... is a sequence defined as follows: 91 = 3, 92 = 5, gk = 3gk-1 - 2gk-2 for…

A:

Q: 5. Describe four different rules for determining le next entries in the sequence that follows. Give…

A:

Q: Suppose that a sequence is defined as follows. a, =7, a,=a,-1-3 for n>2 List the first four terms of…

A: The objective of the question is determine the four terms of the given sequence.

Q: 4. Write down the first six terms of the Fibonacci =1 and F2 = 1. sequence defined by Fn Fn-1 +…

A:

Q: 9. Find the partial sum of arithmetic sequence of 25 terms starting with 5, 10, 15, 20,.........

A:

Q: Terms of the sequence a1, a2, a3, . .. , a2020 are obtained by the rule: 1+a1 1+ a2 1+ a2019 az = 1-…

A: Reciprocal of a number n is 1n.

Q: 3. Find two possible next terms of a sequence 2, 8, 9,17 that is neither geometric nor www…

A: Given the sequence 2,8,9and 17. We need to find the 2 possible next terms of a sequence.

Q: 1. What is the common difference in the sequence 3/4, 5/8, 1/2, 3/8? 2. (identify) It is a graph…

A: We are entitled to solve only one question at a time. Please submit other questions separately. To…

Q: Suppose that the sequence {ax} is =0 2, 4, 6, 8, 10, 12, 14, 16, .. What is a1?

A: The given sequence {ak}k=0∞ is -  {ak}k=0∞ = 2,4,6,8,10,12,14,16,18,......... The first tern of the…

Q: Suppose that the sequence {ax}ı is k= 1,3, 5, 7, 9, 11, 13,.. What is a;?

A:

Q: Suppose ao, a1, a2,... is a sequence such that ao = a1 = 1 and forn2 1, an+1 = n(an+an-1). Find az =…

A:

Q: , n=1,2,3. is a sequence of real numbers defined by a, = /2 %3D %3D and for n21, a = 2,/2+a, .

A:

Q: 7. a) Determine the first 5 terms of the sequence defined by t, = tn-1+ 7,t, = 3,n € N b) Determine…

A: 7. given that

Q: How many ordered sequences are possible that contain 2  objects chosen from 9 ? ​

A:

Q: 1. Which is a finite arithmetic sequence?

A:

Q: 8. Find x such that 9, x, 19 is an arithmetic sequence.

A: If the give sequence is in arithmetic progression, then the common difference between any two…

Q: Suppose that a sequence is defined as follows. a1=-5, a,=4a, +10 for n>2 List the first four terms…

A:

Q: d. If the chosen sequence has a finite number of terms and its sum i are there? e. Express the…

A:

Q: (2) Identify the next likely term in the sequence and the type of sequence: 5000, 2000, 800, 320,…

A: 2. The required sequence can be solved as below

Q: Suppose that bı, b2, bs, is a sequence defined as bk-1+ bk-2 for each integer ... follows: b1 = 4,…

A:

Q: Find the number of length-7 sequences from the numerical digits {0,1,2,3,4,5,6,7,8,9} such that the…

A: Combination(Selection): It refers to the situation where order of occurrence of event does not…

Q: The generating function of the sequence 5,5,5,5,5 is 1-x° (1-x) 1-5x° (1-x) 1- 125x (1-x) 1-3125x…

A:

Q: The five first terms of the sequence {4n–1}=1 are: O 3,7,11,15,19,... O 3+7+11+15+ 19... O…

A:

Q: Show that the sequence too n! 217 is eventually strictly increasing or eventually strictly…

A: The given sequence is n!21nn=1∞ Eventually strictly increasing sequence : A sequence is said to be…

Q: Find the first 4 terms and the eighth term of the recursively defined sequence. C1 = 7, c2 = - 2,…

A:

Q: Suppose that f0, f1, f2, ...  is a sequence defined as follows:  f0 = 5, f1 = 16, fk = 7fk-1 -…

A:

Q: Find the first 4 terms and the eighth term of the recursively defined sequence. C1 = 3, c2 = - 1,…

A:

Q: Suppose that the sequence {az}ı is k=1 1,3, 5, 7,9, 11, 13,.. What is a1?

A: First we find the general of the given sequence {ak}∞k=1=1,3,5,7,9,11,13,..., with the help of…

Q: Find x and y such that 5, x, y,32 is part of an arithmetic sequence. Then find x and y so that the…

A: Given sequence is 5,x,y,32. First find the value of x and y such that sequence 5,x,y,32 is a part of…

Q: 4. Let (bn) be a sequence defined by 4bn-2 - bn-1 n > 2 b, n = 1 -1 n = 0

A:

Q: Find a closed formula for the sequence defined recursively by bo = 2, by = 3 and b, = 3b,-1 – 2b,-2…

A:

Q: 35. Prove that the sequence {n!}^, beats the sequence {2"}-1-

A:

Q: 2. Write a recursive definition for the sequence 14, 10, 6, 2,... Oaj = 14, an = an-1+4 %3D Oa = 2,…

A: To write a recursive defintion for the sequence 14, 10, 6, 2, ...

Q: The sequence {3.1 , 3.12 , 3.123 , 3.1234 , ...} is a bounded sequence. True False

A:

Q: What is the generating function for the sequence {ck},where ck is the number of ways to make change…

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.