01. Prove the following conjecture: The sum of any two consecutive integers can be written in the form 4n +1 where n is some integer. 02. Prove the following conjecture: If n is even, then 7n + 4 is even. 03. Prove by contradiction: Let a , b be the side lengths of a right triangle. Let c be the length of the hypotenuse of the right triangle. Prove c > a +b 04. Prove by contradiction: For all integers n , If n ^ 3 is odd then n is odd.

Q: If the first term of an AP is -10 and the common difference is 2 At which term will the value equal…

A: an = a + (n-1)d  Here a =-10. , d = 2 and an = 0  Then find n

Q: 3.Two projects are proposed in the organization. Out of the 30 members, 14 members like project A,…

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Q: 27. (xa is an odd number between and 9, inclusive}

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Q: 7>12

A: We have to find solution of y

Q: If the largest of 58 consecutive integers is 529, what is the smallest? Write your answer in the…

A: There are 58 consecutive integers. Largest number is 529. That is 58 th observation is 529.

Q: This number has four figures.  They are in consecutive order.  The sum of the digits is 18.  One…

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Q: 4x - 2 s -22

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Q: What is the sum of consecutive whole numbers that begin with 1, increase to 200, and then decrease…

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Q: how to translate the sum of 3 consecutive even integers if the largest is y into a expression

A: Concept: Consecutive numbers are those that come after one another in ascending sequence, from…

Q: If the mean of aneven number of consecutive integers is 0.5, what is the sum of two middle integers?

A: Here, The mean of an even number of consecutive integers is 0.5

Q: < 15 X = 18 4x 2x+6 18

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Q: The sum of the first n terms of a GP is 189. If the first term and the second term of the GP are 3…

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Q: Graph the number on the number line 3.  =6, -1, 0,3 4. -3 1/2, -2.5, 4 3/4

A: 3) Given numbers are,-6, -1, 0, 3

Q: What is the range of the numbers -3,2,-5,3,11?

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Q: The notation 2 < 5 means that 2 is to the of 5 on a number line.

A: The notation 2&lt;5 means that 2 is to the _________ of 5 on a number line.

Q: You purchase boxes of cereal until you obtain one with the collectors toy you want. If on average…

A: Basics:

Q: 6x < -30

A: Given query is to solve the inequality.

Q: -9+b<45 can you help me with this please?

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Q: In order to pass a class, you need an average of 90 on 7 exams. If your test scores were 98, 86, 90,…

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Q: numbers have a sum of 205. If one number is n, represent the other number as an expression of n?

A: Given query is to find the expression for the number in terms of n.

Q: if the five times the fifth term of an AP is equals to 8 time it's eight term.show that the 13th…

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Q: -13<3x-4< 2

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.