The sum of consecutive integers 1, 2, 3,...n is given by the formula 1/2n(n+1). How many consecutive integers, starting with 1 , must be added to get a sum of 703 ?

Q: How many real valued solutions over (-1,1) to the following ODE?

A: given odinary differential equation  y'=x1-y'+ylnlny'+eπxy claim-  to check how many solution does…

Q: A professor gives his students 4 essay questions to prepare for an exam. Only 2 of the questions…

A:

Q: Tennis balls are randomly tossed into one of 5 trays. Determine the number of balls needed to ensure…

A:

Q: On a game show, a secret 4-digit number is formed using the digits 1, 2, 3 and 4, with repetition…

A:

Q: How many 5 digit even numbers are there, a. Given that the first digit cannot be zero. b. Given…

A: In five digit following digit can be filled in following ways: First digit can be filled by…

Q: Use the formula for nCr to solve, An election ballot asks voters to select three city commissioners…

A: There are total 6 people to choose from. So, n=6  And we have to choose 3 people. So, r=3  We know…

Q: Use the formula for nCr to solve, A four-person committee is to be elected from an organization’s…

A: Given that total number of people = n= 11 We have to pick r=4 people from those 11 people.  We know…

Q: The sum of the first n odd numbers is n°; that is, Ź(2x – 1) = n². X=1 Verify this formula for n =…

A: The sum of the first n odd numbers is n2. Then we get, ∑x=1n2x-1=n2 We have to verify the results…

Q: A sequence of positive integers starts with one 1, followed by two 2s, three 3s, and so on. (Each…

A: Given:     The sequence is:     1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,... To get this number, we have to…

Q: There are 20 seats in the front row of a theater. Each successive row contains two more seats than…

A: There are 20 seats in the front row of a theater. Each successive row contains two more seats than…

Q: Find the sum of the first 21 positive integers. The sum of the first 21 positive integers is

A: We will use the concepts of A.P.

Q: When the smallest of three consecutive odd integers is added to four times the largest, it produces…

A:

Q: The formula N= 3x² + 5x + 1 represents the number of households N, in thousands (i.e. if the number…

A:

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: For how many values of n is the sum 1 + 2 + · • + n not divisible by n if 1 ≤ n < 100?

A:

Q: 2. Certain bacteria cells are being observed in an experiment. It was noted that the population…

A:

Q: A small combination lock on a suitcase has 4 wheels, each labeled with the 10 digits 0 to 9 How many…

A: It is given that, a small combination lock on a suitcase has 4 wheels, each labeled with the 10…

Q: The 5th term of an A.P. is 15 and the first term is 3. What is the sum of the first 10 terms?

A:

Q: How many four-digit numbers can be formed from the digit 0, 1, 2, 3, 4,5, 6, 7, 8 ,9 if each digit…

A: Here use combination

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

A: Assuming that both letters and numbers can be repeated. Since A letter can be choose  in 26 ways and…

Q: A certain number is doubled and then divided by 8. If after subtracting 4 from this result, one gets…

A: The statements involving algebraic operations and expression namely addition , subtraction ,…

Q: Find all the odd positive integers n which satisfy 6(n) = 20.

A:

Q: 11.) The sum of four consecutive even integers is 68. Find the four consecutive even integers. What…

A: We know that an even integer is always divisible by 2. Let the first even integer in the consecutive…

Q: John is twice as old as his friend Peter. Peter is 5 years older than Alice. In 5 years, John will…

A: Consider John's age as J, Peter age's as P and Alice age as A. From given, J=2P, P=A+5 and J+5=3A.

Q: Any n consecutive integers will include a number that is divisible by n.

A:

Q: A small combination lock on a suitcase has 3​wheels, each labeled with the 10 digits 0 to 9. How…

A:

Q: A plant grows 5 inches taller each day. During a period of 3 days, how many different values will…

A: Explanation of the answer is as follows

Q: With a short time remaining in the​ day, a delivery driver has time to make deliveries at 5…

A: Combination:Combination is defined as the selection of all or part of a set of objects, without…

Q: The digits 1, 2, 3 and 4 can be arranged to form different four-digit codes. a. Find the number of…

A:

Q: The sum of a sequence of consecutive integers is 342. The largest integer in the sequence is 3 times…

A:

Q: Two integers, a and b, have a product of 48. What is the least possible sum of a and b? The least…

A: Answer is a+b= -49. Explanation is given below...

Q: For how many integers between 1000 and 9999 is the sum of the digits exactly 9? How many of them…

A: Note:  As per bartleby instruction when more than one question is given only one has to be answered.…

Q: A new square is formed by joining the midpoints of the consecutive sides of a square 8 inches on a…

A:

Q: For n ≥ 2, let an=5n/n2-2 Determine for which n, |an|<1

A: Use the given inequality for an and find the quadratic equation for n and solve

Q: Find the least natural number a with the property that the sum a + 2a + 3a + .. + 9a is the number…

A: Given sum is  a+2a+3a+4a+5a+6a+7a+8a+9a

Q: For n≥2, let an= 5n/n2-2. Determine for which n, |an|<1.

A: Use the inequality on and find the inequality for n

Q: how many positive integers n satisfy 22-5n>-3?

A: 22-5n&gt;-3

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

A:

Q: Solve for N 3n + 8= 20

A: Given, Solve for n 3n +8 = 20

Q: Solve for n: 8n-5 2n + 10

A:

Q: The nth term formula for the maximum number of pieces of baked cheese cake, Pn, that can n(n+1) be…

A: Given that , Maximum number of pieces of baked cheese cake Pn=nn+12 where n is number of straight…

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

A: We're going to solve

Q: Two consecutive terms in the expansion of (a + 2b)20 are equal. Find these terms.

A: Given:(a+2b)20 The general r+1 th term in the above expansion can be written as, Tr+1=20Cra20-r(2b)r…

Q: With a short time remaining in the day, a delivery driver has time to make deliveries to 6 different…

A:

Q: The fourth term of an A.P. is equal to 3 times of the first term and the seventh term exceeds twice…

A: let first term a , and common difference = d  now according to the question

Q: The sum of the consecutive integers 1, 2, 3, cn is given by the formula 1/2n(n + 1). How many…

A: Given: The sum of the consecutive integers 1, 2, 3,..., n is given by the formula: S=12n(n+1)

Q: The sum of the four positive integers a, b, c, and d is at most 10. Find the number of possible…

A: Explanation of the answer is as follows

Q: If the sum of n successive odd natural numbers starting from 3 is 48 , Find the value of n

A: