What is the sum of two consecutive numbers the difference of whose squares?
Table of Contents
- 1 What is the sum of two consecutive numbers the difference of whose squares?
- 2 What is the sum of two consecutive odd numbers the difference of whose squares is 104?
- 3 What is the sum of the first 16 odd numbers?
- 4 What is the sum of squares of odd numbers?
- 5 What is the difference between the squares of two consecutive integers?
- 6 Is the difference of the squares of two odd numbers divisible by 4?
What is the sum of two consecutive numbers the difference of whose squares?
Answer: The sum of the two consecutive numbers 9 and 10 be 19. Given that, the difference of their squares will be 19.
What is the sum of two consecutive odd numbers the difference of whose squares is 104?
The two consecutive odd integers that will add up to 104 are: 51 and 53.
What is the difference between two consecutive even numbers?
For any two consecutive even numbers, the difference is 2. For example, 6 and 8 are two consecutive even numbers, their difference = 8 – 6 = 2. For example, the sum of these 3 consecutive numbers is 5+6+7=18 and 18 is divisible by 3.
What is the sum of the first 16 odd numbers?
Therefore, 256 is the sum of first 16 odd numbers.
What is the sum of squares of odd numbers?
Sum of Squares of First n Odd Numbers
| Sum of: | Formula |
|---|---|
| Squares of three numbers | x2 + y2+z2 = (x+y+z)2-2xy-2yz-2xz |
| Squares of first ‘n’ natural numbers | Σn2 = [n(n+1)(2n+1)]/6 |
| Squares of first even natural numbers | Σ(2n)2 = [2n(n+1)(2n+1)]/3 |
| Squares of first odd natural numbers | Σ(2n-1)2 =[n(2n+1)(2n-1)]/3 |
How do you find the difference between two consecutive odd squares?
The difference between the squares of two consecutive odd integers is always divisible by Let two consecutive odd integers be = 2k +1 and 2k +3, where k is any integer. Now, (2k + 3) 2 – (2k + 1) 2 = (4k 2 + 9 + 12k) – (4k 2 + 1 + 4k)
What is the difference between the squares of two consecutive integers?
In general, if you have the difference of two consecutive squares, Thus, our two numbers are 17 and 18. Originally Answered: The difference between the squares of two consecutive integer is 35. What are the numbers?
Is the difference of the squares of two odd numbers divisible by 4?
Prove or disprove that the difference of the squares of two odd numbers is always divisible by 4. No idea how to use the proving method to solve this. elementary-number-theory Share Cite Follow edited Aug 24 ’15 at 18:10 ajotatxe 62k22 gold badges5050 silver badges9999 bronze badges asked Aug 24 ’15 at 18:09 HeellopppHeelloppp
Is a D difference of two squares a multiple of 4?
Clearly, a + b and a − b at either both even or both odd. So a d difference of two squares is either of our a multiple of 4. In fact, if N is odd or a multiple of 4, then we can always find a, b such that N = a2 − b2: if N is odd, take a = (N + 1) / 2 and b = (N − 1) / 2, and if N is sa multiple of 4, take a = N / 2 + 1 and b = N / 2 − 1.