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
none - see previous post.
To determine which of the given expressions are divisible by 4 for all natural numbers n, we need to test each expression individually.
1. 5n + 1 - 9:
Notice that this expression simplifies to 5n - 8. In order for 5n - 8 to be divisible by 4, the coefficient of n (i.e., 5) should be divisible by 4. However, since 5 is not divisible by 4, this expression is not divisible by 4 for all natural numbers n.
2. 6n - 2:
Looking at this expression, we can see that all the terms are divisible by 2. Since 6n is divisible by 2, and 2 is divisible by 2, this expression is divisible by 2. However, it is not necessarily divisible by 4 because 6 is not divisible by 4.
3. 7n + 1:
Similar to the first expression, for 7n + 1 to be divisible by 4, the coefficient of n (i.e., 7) should be divisible by 4. However, 7 is not divisible by 4, so this expression is not divisible by 4 for all natural numbers n.
4. 3n + 1:
Again, similar to the previous two expressions, for 3n + 1 to be divisible by 4, the coefficient of n (i.e., 3) should be divisible by 4. However, 3 is not divisible by 4, so this expression is not divisible by 4 for all natural numbers n.
5. 10n - 2:
Looking at this expression, we can see that all the terms are divisible by 2. Since 10n is divisible by 2, and 2 is divisible by 2, this expression is divisible by 2. Additionally, since 10 is divisible by 4 (10 divided by 4 equals 2 remainder 2), this expression is divisible by 4 for all natural numbers n.
In conclusion, the only expression that is divisible by 4 for all natural numbers n is 10n - 2.