The sum of the consecutive integers 1, 2, 3, cn is given by the formula 1/2n(n + 1). How many consecutive integers, starting with 1, must be added to get a sum of 666?

Q: 10. Twice a number decreased by four is greater than ten, what numbers satisfy this condition?

A:

Q: Joy invests a total of $6000 in two accounts paying 5% and 11% interest, respectively. How much was…

A: Given, investment amount = $ 6000 Joy got a total interest for the year =$570 The interest rate for…

Q: Christine is 41 years old and her daughter is 9. In how many years will Christine will be there…

A: Given data: Christine is 41 years old and her daughter is 9. To find: In how many years will…

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: In a class experiment, a student needs 5 Liters of 6% solution. He found a 4% and a 10% solution in…

A: Let a=Volume in liters of 4% solutionand b=Volume in liters of 10% solution.Therefore, a+b=5⇒b=5-a

Q: How many ways can the letters of the word "EQUATION" be arranged if “NOTI" must b next to each other…

A: Here  use concept of arrangement

Q: How far from the base of the house do you need to place a 15’ ladder so that it exactly reaches the…

A:

Q: How many solutions are there to the equation a + b + c + d + e = 505 if each of a, b, c, d, and e is…

A:

Q: Phineas can build a rocket in 7 hours while Ferb can do the same work in 14 hrs. If they work…

A: Given, Phineas can build a rocket in 7 hours, Ferb can do the same work in 14 hrs.  They together…

Q: 3) The sum of three consecutive even integers is 48. Find the integers

A:

Q: Bob is 2 years from being twice as old as Ellen. The sum of twice Bob’s ageand three times Ellen’s…

A:

Q: How many liters of 50% alcohol solution and 20% alcohol solution must be mixed to obtain 12 liters…

A: To determine the volume of each solution used.

Q: The sum of the first n natural numbers, S = 1 + 2 + 3 + first n natural numbers is 171, determine…

A: Consider the given information:

Q: 1) The sum of three consecutive even integers is 768. Find the integers.

A: Solve to find the integers

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

A:

Q: John is x years old . Stacy is 2 years less than twice John’s age . Together, their ages sum to 19 .…

A: Given John's age='x' year Stacy's age=2x-2

Q: In a class of 60 students,each of the students passed either in mathematics or in science or in…

A: Given: Total number of students passed either in mathematics or in science or in both=60 Students…

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…

A:

Q: Use the formula for nCr to solve, There are 14 standbys who hope to get seats on a flight, but only…

A: Formula used: Crn=n!(n-r)!r!

Q: After my birthday in the year 2010, the number of my years was the same as the sum of digits of the…

A:

Q: 4) The sum of two consecutive even integers is at most 400. Find the pair of integers with the…

A: Assume   Two Even integers are 2n and 2n+2 as per condition : (2n)+(2n+2)≤4004n+2≤4004n≤398n≤99.5

Q: Solve for n. 56 -1 P=n+1 P,

A: We can find n by using the following equation.

Q: A person and plans to invest a total of $6500 in one bank account at 6.3% annual interest and…

A:

Q: In a GP the 6th term is 16 and the 3rd term is 128. Find the sum of the first 10 terms and the sum…

A: A geometric progression or a geometric sequence is a sequence of non zero numbers, where each terms…

Q: Solve for n: 6n 20 2n + 4 (1 3n) Зп)

A:

Q: With two reapers operating, a field can be harvested in 1 h. If only the newer reaper is used, the…

A: Time taken by both the reapers working together is 1 h. Thus, work done by both the reapers is,…

Q: Currently, Trevon is three times as old as Janice. In four years, the sum of their ages will be 48.…

A:

Q: Solve: If n is a known positive integer for what number c is (xn-1dr =

A:

Q: A woman decides to go for a 10-minute run every day this week and plans to increase the time of her…

A: For first week =10 min Increment of time every week =4 min common difference=4

Q: Solve the PDE of the first order и, — и, — 0, и(х,Зх) — 2? и (х, Зг) — Ur – = x

A: Given problem is :

Q: Samuel can clean the house in 4 hours. Mya can clean the same house in 3 hours. How long would it…

A:

Q: The sum of a certain number of consecutive non-negative integers is 2500. Can you find an example of…

A: Let a be the first integer. If there is one integer then sum is a Since, number is consecutive, then…

Q: Find the number between 1/2 and 3/2 such that the sum of this number and its reciprocal is as big as…

A: The numbers between 12 and 32 or 0.5 and 1.5 are as follows: 0.6, 0.7, 0.8, 0.9, 1, 1.2, 1.3, 1.4…

Q: A group of people share equally in a $5,000,000 lottery. Before the money is divided, three more…

A: It is given that,a group of people share equally in a $5,000,000 lottery. Before the money is…

Q: Mary is 24 years old. Mary was twice as old as Ann was when Mary was as old as Ann is now. How old…

A: Note: There is mistake in statement as, statement talks about past in both part. which will not…

Q: Solve the problem. 1) Aaron invested a total of 8 4,100, some in an account earning 8% simple…

A: According to the question, Aaron invested some money earning a interest of 8% and the rest of the…

Q: 1. The sum of three consecutive odd integers is 27. Find the three integers.

A: As per the company guidelines We can answer first question . Please understand. Kindly repost the…

Q: Patrice has worked a certain amount of hours so far this week. Tomorrowshe will work four more hours…

A: Let us assume that Patrice has worked for N hours so far.

Q: At Janice's current age she is not only 5 times as old as Ross, but she is also 28 years older than…

A:

Q: In an AP the sum of first n terms is (3n2 /2) + (5n/2) . Find its 25th term

A:

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

A:

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

A: the grains keep multiplying by 2 on each box On the second square the king would place 2 grains of…

Q: 1) The sum of four consecutive integers is 462. Find the integers.

A: GIVEN: The sum of 4 consecutive integers is 462

Q: the time to complete each task of the project was estimated to require 3 workers for 4 months, but…

A:

Q: A tank can be filled by 2 water keys together in 3 hours with 3 quarters. The main key would be able…

A: Given: -

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: given a starting population of 100 bacteria, the formula b=100(2)^t can be used to find the number…

A:

Q: The first year, two cows produced 8100 liters of milk. The second year, their production increased…

A: Given :           Let cow 1 produce x litres in year 1           Let cow 2 produce y litres in year…

Q: A man’s age is 36 and that of his daughter is 3 years. In how many years will the man be 4 times as…

A: Man's age = 36 Daughter's age = 3  Let after x years man will be 4 times as old as his daughter

Q: In the year 2010, a person bought a new car for $29000. For each consecutive year after that, the…

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.