If in an AP the sum of m terms is equal to n and the sum of n terms is equal to m .then prove that the sum of (m+n) terms is -(m+n)

Q: Suppose that a1, a2, a3, a4 are four numbers. 4 If > ak -9 then (3ak +5) is equal to.. k=1

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Q: If the 10 term of an AP is 21 and the sum of its first ten terms is 120 find its n term

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Q: A student needs 8 more classes to complete her degree. If she has met 5 pre-requisites for all the…

A: A student needs 8 more classes to complete her degree. If she has met 5 pre-requisites for all the…

Q: For this problem, assume there are 9 adjacent seats in a row. How many different ways can 9 people…

A: 9! = 9*8*7*6*5*4*3*2*1 = 362880

Q: In a family of cats, there are 2 un-cool cats for every 3 cool cats. If these cats have 120 paws…

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Q: How many teams of 4 can be chosen from a group of 15 adults and 10 children if each team must have…

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Q: The sum of any two integers of the from 4k+ is always: a) prime b) zero c) Even

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Q: If 17th term of an AP exceeds its 10th term by 7 , Find the common differenc

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Q: A cube of 5 cm is painted on all its faces .If it is sliced into 1 cubic centimetre cubes , how many…

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Q: The 24th term of an AP is twice its 10th term .Show that its 72th term is 4 times its 15th term

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Q: In the past, a local telephone number in a country consisted of a sequence of three letters followed…

A: The telephone numbers consist of sequences of 2 letters followed by 5 digits and 3 letters are…

Q: A king in ancient times agreed to reward the inventor of chess with one grain of wheat on the first…

A: According to the given information, the king is rewarding the inventor of chess with grains of wheat…

Q: A and B can do a piece of work in 3 days, B and C in 4 days, while A and C in 2.5 days. In how many…

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Q: A boy imagined four-digit multiple of 5 with different digits. If the first digit is erased, the…

A: Suppose the number be xyzw and x,y,z,w are different numbers. Now the number is multiple of 5. so W…

Q: Prove that given any set of eight integers, there is a pair among them whose sum or difference is…

A: Let n1,n2,n3,n4,n5,n6,n7,n8 be the 8 integers. Let ni≡rimod12 where 0≤ri<12 Suppose, no two of…

Q: There are ducks and pigs in a farm. Together, there are 35 heads and 100 legs. Assuming that each…

A: Simplification

Q: A theater hall has n rows of seats. The first row has 25 seats, the second row has 33 seats, and the…

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Q: selected from a group of 11 Republicans and for Democrats. Find the number of ways of obtaining a…

A: Given that   Committee consists of members (r) = 7 Committee need to be selected from group of 11…

Q: Suppose you must use 1x“-tile and 10 x-tiles. You only have up to 15 1-til use. How many of the…

A: Introduction: A rectangle is a quadrilateral with equal angles and opposite sides that are equal and…

Q: 4) The sum of the first 10 terms, let the first term be (a)and the common difference (d), then the…

A: Given , The 8th term is given by 23 and a11=4a3  To find the sum of 10 terms is 155.

Q: Suppose any possible arrangement of 8 letters is considered a word and the letters are chosen from…

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Q: What is the largest number x such that x<200 and x has exactly 4 factors?

A: Factors:    Number that are multiplied together to get a product                              Factor…

Q: How many integer solutions are there to x1+ x2 + x3 = 0  with Xi >= -5 ?

A: We need to find the integer solutions to x1+x2+x3=0 such that each of the three numbers is greater…

Q: Find the sum of positive divisor of 5,020 and also find the pair of this number so that they can be…

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Q: If product of two consecutive odd integers is 63, then the integers are: 7, 9 9, 11 7, 11 7, 13

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Q: Suppose that 9 people lost an average of 13.3 pounds over the course of the first month of being on…

A: 9 people lost 13.3 pounds on an average. Let w1,w2,...,w9 be the weight loss of the 9 people. Then…

Q: If there are x teams in a league and each team plays every other team twice, then the total…

A: Quadratic equation : A quadratic equation is any equation that can be rewritten in standard form as…

Q: Show that there are infinitely many examples of two consecutive positive integers that cannot be…

A: According to the given information, It is required to prove that there are infinitely many examples…

Q: When 32 is divided by an integer, the remainder is 4. When 51 is divided by the same integer, the…

A: We can use concept of HCF to solve the problem

Q: If the sum of a certain number of terms starting from first term of an AP is 25,22,19,,,....,,is 116…

A: A.P is of the form 25,22,19, ... Here first term =a = 25 Common Difference = d = 22-25 = -3 Sum of n…

Q: Show A and Show B are two of the most popular television shows of all time. The number of episodes…

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Q: Show that you can make four distinct lists of books so that the total number of pages in the books…

A: Given: 15 text books is available and each with between 200 and 600 pages

Q: A medical student has to work in a hospital for five days in January.  However, he is not allowed to…

A: there are 31 days in January Out of 31 days , student has to work 5 days therefore the non working…

Q: John found the sum of the first 2021 positive even integers and Bob found the sum of the first 2022…

A: In this question, tne concept of sum of first positive even integers is applied.

Q: If n∈N and n<2000 , how many numbers n have the property that the sum of the digits of n and the sum…

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Q: How can the sum of k * (n choose k) = n(2 to the power of n-1) be proven akgebraically ?

A: Step 1: We have to prove that, Now by the binomial theorem, Now, differentiating the both sides of…

Q: in 2  rows  there are  5 armchairs  and all are  occupied , in how many  differnt  ways can theses…

A: Given: Number of Rows =2. Number of armchair = 5. To determine the number of ways substitute the…

Q: If n EN and n < 2000, how many numbersn have the property that the sum of the digits of n and the…

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Q: Suppose that a1, a2, a3, a4, a5 are five numbers. 5 If ak =-7 then (2ak + 3) is equal to... k=1 k=1

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Q: Find the number of ways in which 6 teachers can be assigned to 4 sections of a math course if no…

A: Solution: 5. From the given information, there are 6 teachers and 4 sections.

Q: The sum of an integer and 4 less than that integer is even.

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Q: Find five consecutive odd integers such that when the fifth is subtracted from eigt times the…

A: We're going to solve

Q: If the sum of the digits is divisible by 2, then the number is divisible by 2. true or false

A: If the sum of the digits is divisible by 2, then the number is divisible by 2.

Q: If the sum of first 7 terms of an A.P is 49 and that of 17 terms is 289,find the sum of first n…

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Q: If n EN and n < 2000, how many numbers n have the property that the sum of the digits of n and the…

A: Given: n∈ℕ And n&lt;2000

Q: Suppose a department contains 12 men and 15 women. How many ways are there to form a committee with…

A: According to the question  number of combination are

Q: How do I solve for A in (4-Ax3=7-Ax6)

A: Add Ax^6 to both sides.

Q: Let ab5c be all four-digit multiples of number 36 with different digits. If someone found 7 numbers…

A: Let ab5c be all four digit multiples number 36 with different digits. As 36= 4x9, so the number ab5c…

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.