Which of following is divisible by 4 for all natural numbers n? (Select all that apply.)
please help ?!?!?
5n + 1 − 9
6n − 2
7n + 1
3n + 1
10n − 2
I don't see any which work
5(1)+1-9 = -3
6(4)-2 = 22
7(2)+1 = 15
3(2)+1 = 7
10(2)-2 = 18
To check which of the expressions is divisible by 4 for all natural numbers n, we need to find a pattern or rule that satisfies this condition for all possible values of n.
Let's go through each option and apply the rule to see if it holds:
1) 5n + 1 − 9
To check if this expression is divisible by 4, we can simplify it:
5n + 1 − 9 = 5n - 8
Since the simplified expression does not have a fixed value, it does not appear to be divisible by 4 for all natural numbers n.
2) 6n − 2
To check if this expression is divisible by 4, we can simplify it:
6n - 2
We can rewrite this expression: 6n - 2 = 6n - 4 + 2.
Since 6n - 4 is divisible by 4 for all natural numbers n, and adding 2 to a number divisible by 4 does not change divisibility, we can conclude that this expression is divisible by 4 for all natural numbers n.
3) 7n + 1
To check if this expression is divisible by 4, we can simplify it:
7n + 1
Since the simplified expression does not have a fixed value, it does not appear to be divisible by 4 for all natural numbers n.
4) 3n + 1
To check if this expression is divisible by 4, we can simplify it:
3n + 1
Since the simplified expression does not have a fixed value, it does not appear to be divisible by 4 for all natural numbers n.
5) 10n − 2
To check if this expression is divisible by 4, we can simplify it:
10n - 2
We can rewrite this expression: 10n - 2 = 10n - 4 + 2.
Since 10n - 4 is divisible by 4 for all natural numbers n, and adding 2 to a number divisible by 4 does not change divisibility, we can conclude that this expression is divisible by 4 for all natural numbers n.
Based on our analysis, the expressions that are divisible by 4 for all natural numbers n are:
- 6n − 2
- 10n − 2