consecutive integers

Take two consecutive integers: n, n + 1 The difference of their cubes is: (n + 1)^3 - n^3 n^3 + 3n^2 + 3n + 1 - n^3 Cancel the n^3 3n^2 + 3n + 1 Factor out a 3 from the first 2 terms: 3(n^2 + n) + 1 The first two terms are always divisible by 3 but then the + 1 makes this expression not...

Take an integer n. The next consecutive integer is n + 1 Subtract the difference of the squares: (n + 1)^2 - n^2 n^2 + 2n + 1 - n^2 n^2 terms cancel, we get: 2n + 1 2 is even. For n, if we use an even: we have even * even = Even Add 1 we have Odd 2 is even. For n, if we use an odd: we have...

The difference between the squares of two consecutive numbers is 141. Find the numbers Take two consecutive numbers: n- 1 and n Given a difference (d) between the squares of two consecutive numbers, the shortcut for this is: 2n - 1 = d Proof of this: n^2- (n - 1)^2 = d n^2 - (n^2 - 2n + 1) =...

If two consecutive even numbers are added, the sum is equal to 226. What is the smaller of the two numbers? Let the smaller number be n. The next consecutive even number is n + 2. Add them together to equal 226: n + n + 2 = 226 Solve for n in the equation n + n + 2 = 226 Step 1: Group the n...

What is the average of 7 consecutive numbers if the smallest number is called n? First number = n Second number = n + 1 Third number = n + 2 Fourth number = n + 3 Fifth number = n + 4 Sixth number = n + 5 Seventh number = n + 6 Average = Sum of all numbers / Total numbers Average = (n + n...

What is the sum of four consecutive multiples of 5? First number = n Second number = n + 5 Third number = n + 10 Fourth number = n + 15 Add them together: (n + n + n + n) + (5 + 10 + 15) 4n + 30

There are five consecutive numbers and the smallest is called n. What is the largest number called? List out consecutive numbers. Each consecutive number is found by adding 1 to the prior number n n + 1 n + 2 n + 3 n + 4

The sum of 3 consecutive integers is greater than 30. Let the first consecutive integer be n The second consecutive integer is n + 1 The third consecutive integer is n + 2 The sum is written as: n + n + 1 + n + 2 Combine like terms: (n + n + n) + (1 + 2) 3n + 3 The phrase greater than means...

sum of 3 consecutive odd integers equals 1 hundred 17 The sum of 3 consecutive odd numbers equals 117. What are the 3 odd numbers? 1) Set up an equation where our odd numbers are n, n + 2, n + 4 2) We increment by 2 for each number since we have odd numbers. 3) We set this sum of consecutive...

The sum of twice an integer and 3 times the next consecutive integer is 48 Let the first integer be n This means the next consecutive integer is n + 1 Twice an integer means we multiply n by 2: 2n 3 times the next consecutive integer means we multiply (n + 1) by 3 3(n + 1) The sum of these...

4 consecutive integers such that the sum of the first 3 integers is equal to the 4th Let n be our first consecutive integer. n n + 1 n + 2 n + 3 The sum of the first 3 integers is equal to the 4th: n + n + 1 + n + 2 = n + 3 Simplify by grouping like terms: (n + n + n) + (1 + 2) = n + 3 3n +...

the left and right page numbers of an open book are two consecutive integers whose number is 235 find the page numbers Using our consecutive integer calculator, we get: 117, 118

Three good friends are in the same algebra class, their scores on a recent test are three consecutive odd integers whose sum is 273. Find the score In our search engine, we type in 3 consecutive integers whose sum is 273 and we get: 90, 91, 92

The sides of a triangle are consecutive numbers. If the perimeter of the triangle is 240 m, find the length of each side Let the first side be n. Next side which is consecutive is n + 1 Next side which is consecutive is n + 1 + 1 = n + 2 So we have the sum of 3 consecutive numbers is 240. We...

The sum of two consecutive integers if n is the first integer. consecutive means immediately after, so we have: n n + 1 The sum is written as: n + n + 1 Grouping like terms, we have: (n + n) + 1 2n + 1

If first integer is 5y, then the next two consecutive integers are integers increase by 1, so we have: 5y + 1 5y + 1 + 1 = 5y + 2

If n represents an odd integer what represents the previous smaller odd integer Each odd integer is 2 away from the last one, so the previous smaller odd integer is found by subtracting 2 from n: n - 2

Let n be the middle number of three consecutive integers This means: n is the second of three consecutive integers The first consecutive integer is n - 1 The third consecutive integer is n + 1 The sum is found by: n - 1 + n + n + 1 Simplifying, we get: (n + n + n) + 1 - 1 3n

Find two consecutive integers if the sum of their squares is 1513 Let the first integer be n. The next consecutive integer is (n + 1). The sum of their squares is: n^2 + (n + 1)^2 = 1513 n^2 + n^2 + 2n + 1 = 1513 2n^2 + 2n + 1 = 1513 Subtract 1513 from each side: 2n^2 + 2n - 1512 = 0 We have...

Consecutive odd integers are odd integers that differ by ______ , such as ______ and 13. Consecutive even integers are even integers that differ by ______ , such as 12 and ______ . Consecutive odd integers are odd integers that differ by ___2___ , such as ___11___ and 13. Consecutive even...