A finite sequence of numbers is called AWESOME if each subsequent member of the sequence, except the first one, is larger than the previous one and if the product of all the members of that sequence is a perfect square. For example, sequence 2,6,27 is an AWESOME sequence. Determine the natural numbers x and y such that the sequence 28,x,y,65 is

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A: The given interval is (-1/n,2-1/n) where natural number n belongs to positive integers. So that we…

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Q: Find a sequence of elementary mateices, that can of ele mentary matcices that can be used to lwrite…

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Q: questionCompute P5,4

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Q: A bit string is a finite sequence of O's and 1's. How many bit strings of length 9 begin with 10 and…

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Q: Find recurrence relations that describe the following sequences. 1, 4, 13, 40, 121 . . . . 1, -3,…

A: Look for a common pattern that the sequence follows.

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Q: For each of these sequences find a recurrence relation satisfied by this sequence. (The answers are…

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A: Let the length of the side of each square cut off from the corners be xcm.

Q: Suppose that the closed formula for a sequence is a polynomial formula of degree 4. What can you say…

A: Suppose that the closed formula for a sequence is a polynomial formula of degree 4. If the terms of…

Q: Show that an integer N is divisible by 9 if and only if the sum of its digits is divisible by 9

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A: The length of side of original square is 1. So it's area = 1

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Q: Find The Least Natural Number a With The Property That The Sum a + 2a + 3a +...+ 9a Is The number…

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Q: A finite sequence of numbers is called AWESOME if each subsequent member of the sequence, except the…

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Q: Using Extended Euclidean Algorithm, show that we can write 17 as a linear combination of 119 and 68

A: Extended Euclidean Algorithm- It is a method to find GCD of two integers To write:17 as a linear…

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

A: We can either use trial and error and check all possibilities or try to make to logical deductions.

Q: Find the sum of the positive even integers up to and including 50.

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Q: 3. A bit string is a finite sequence of 0’s and 1’s. For this problem, you may leave your answers…

A: answer(a) 15C6 = 15!/6!(15-6)! =5005 ( bit strings of length 15 having exactly 6 zeros)

Q: A ternary string is a sequence of 0's, 1's and 2's. Just like a bit string, but with three symbols.…

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Q: A knight on a chessboard can move one space horizontally (in either direction) and two spaces…

A: Consider the provided question, We have to proof: The knight can visit every square. Proof by…

Q: A sequence c0,c1,c2,.... is defined by letting c0=3 and ck=(ck-1)2 for every integer k > 1.  Show…

A: Let's write some initial terms of the sequence and observe the pattern.

Q: (uA)ū and u(Av) as sums of products of the entries

A: Note: Here we are solving problem 5.a) for reaming problem please submit the question again. Given:…

Q: A bit string is a finite sequence of O's and l's. How many bit strings have length 9? bit strings…

A: The number of bit strings in each case are found as shown below.

Q: For the infinite geometric sequence (xn) whose first four terms are 2.6,  -5.72,  12.584,  -27.6848…

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Q: that every Positive integer Written as a Sum the fibonacci Sequence Prove can be OF of distinct…

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Q: Which of the facts/claims were used to justify the Euclidian Algorithm? Choose all that apply. O…

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Q: 6. Each of the three vertices of a triangle is connected by n line segments to n distinct points on…

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Q: (a) A bit string is a finite sequence of O's and 1's. How many bit strings have length 77 bit…

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Q: 6. (a) Show, using the pigeonhole principle, that in any set of 5 integers, at least two have the…

A: (a) Show that any set of 5 integers at least have two the same remainder when it is divided by 4…

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Q: Prove: Any positive integer can be represented as an aggregate of different powers of 3, the terms…

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Q: For the sequence 2, 9, 16, 23, 30, 37, 44, 51... find (a) closed formula (b) recurrence relation and…

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Q: If G1 and G2 are isomorphic, must they have the same degree sequence? If G1 and G2 have the same…

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Q: There are three natural number that are less than one thousand that are both perfect square and…

A: Consider the first ten cube numbers 1, 8, 27, 64, 125, 216, 343, 512, 729 and 1000. Check how many…

Q: The Infinite Monkey Theorem states that a monkey hitting keys completely at random on a typewriter…

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Q: There is a sequence a0, a1, a2,……. Which satisfies the recurrence relation ak=6ak-1- 9ak-2 for k≥2.…

A: Consider the recurrence relation: ak=6ak-1-9ak-2 To solve, ak=6ak-1-9ak-2ak-6ak-1+9ak-2=0The…

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Q: Two integers are of the same parity if they are both even or both odd. Prove that if x and y are of…

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Q: A whole number a is odd if and only if there is a whole number k such that a=2k+1. Use this…

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Q: 8. The number is such that when it is divided by 8, it gives a perfecct cube but not a perfect…

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Q: ________________ draws from the box, there is more than 50% chance for a red marble to appear at…

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Q: There is a sequence a0, a1, a2,……. Which satisfies the recurrence relation ak=5ak-1- 6ak-2 for k≥2.…

A: There is a sequence a0, a1, a2,……. which satisfies the recurrence relation ak = 5ak-1 - 6ak-2 for…

Q: a) Find a recurrence relation that would determine the number of sequences a1, a2, ., an that have…

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Q: Which of the facts/claims were used to justify the Euclidian Algorithm? Choose all that apply. O…

A: We know that, Definition of Euclidean algorithm:  a method of finding the greatest common divisor of…

Q: If {v} is a generator sequence then the sequence "-","+" is also a generator sequence.

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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.