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What is the greatest whole number that MUST be a factor of the sum of any six consecutive positive odd numbers?
Let the first odd number be 2n-5 (n ≥ 3), then the 6 consecutive odd numbers are: 2n-5, 2n-3, 2n-1, 2n+1, 2n+3, 2n+5 And their sum is: 2n-5 + 2n-3 + 2n-1 + 2n+1 + 2n+3 + 2n+5 = 12n The greatest common factor for all n(≥ 3) of 12n is 12. Thus 12 is the greatest whole number that MUST be a factor of the sum of any six consecutive positive odd numbers.
Is the sum of an even whole number and an odd whole number always odd?
Yes --------------------------------------------- Let n be an integer. Then 2n is an even number Let m be an integer. Then 2m is an even number and 2m + 1 is an odd number. Then: even + odd = (2n) + (2m + 1) = (2n + 2m) + 1 = 2(n + m) + 1 = 2k + 1 (where k = m + n) which is an odd number.
Twice what number is equal to three times that number?
let the number be n. Then: 2n = 3n ⇒ 2n - 2n = 3n - 2n ⇒ 0 = n ie, the number is zero.
What is the formula for finding the nth hexagonal number?
The nth hexagonal number is given by the formula: hn = 2n * (2n - 1) / 2
What does the term 2N mean?
2n is the diploid number. It double the number of chromosomes present in a genome. 2n represents the number of chromosomes in a somatic cell. The number n is called the haploid number. n represents the number of chromosomes present in a germ cell
What is the name given to all the numbers that can be expressed as the sum of two consecutive whole numbers?
Odd. For any given whole number n, the sum of it and the next whole number is 2n+1. Since 2n is obviously a multiple of 2 and therefore even, 2n+1 must be odd.
What is the greatest whole number that MUST be a factor of the sum of any six consecutive positive odd numbers?
Let the first odd number be 2n-5 (n ≥ 3), then the 6 consecutive odd numbers are: 2n-5, 2n-3, 2n-1, 2n+1, 2n+3, 2n+5 And their sum is: 2n-5 + 2n-3 + 2n-1 + 2n+1 + 2n+3 + 2n+5 = 12n The greatest common factor for all n(≥ 3) of 12n is 12. Thus 12 is the greatest whole number that MUST be a factor of the sum of any six consecutive positive odd numbers.
Is the sum of an even whole number and an odd whole number always odd?
Yes --------------------------------------------- Let n be an integer. Then 2n is an even number Let m be an integer. Then 2m is an even number and 2m + 1 is an odd number. Then: even + odd = (2n) + (2m + 1) = (2n + 2m) + 1 = 2(n + m) + 1 = 2k + 1 (where k = m + n) which is an odd number.
A sum of a number and twice its number?
If the number is n, then twice the number is 2n and the sum of the two is n + 2n = 3n.
Twice what number is equal to three times that number?
let the number be n. Then: 2n = 3n ⇒ 2n - 2n = 3n - 2n ⇒ 0 = n ie, the number is zero.
What does the expression diploid 2n number mean to you?
Every number multiplied by 2 is an even number, so that 2n is an even number. Usually we represent an even number by 2n.
What is the largest possible number of parallel sides in a polygon?
The polygon may have 2n sides, where n is any whole number greater than 1
Why does an even number plus to odd number equal to odd?
Any even number can be written in the form 2n for some natural number n.Any odd number can be written as 2n+1 for a natural number nNow add an even to an odd.2n+2n+1=4n+1 which is 2(2n)+1 and this is the form for an odd number.
What is the formula for finding the nth hexagonal number?
The nth hexagonal number is given by the formula: hn = 2n * (2n - 1) / 2
The two leading digits of each 4-digit number are not shown which number is divisible by 4?
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What is difference between the n and 2n number?
2n is 2 times n.
What does the term 2N mean?
2n is the diploid number. It double the number of chromosomes present in a genome. 2n represents the number of chromosomes in a somatic cell. The number n is called the haploid number. n represents the number of chromosomes present in a germ cell
