Question 474907: How many integers from -8000 to 8000 are divisible by 4?
Please explain how I could approach and solve this, thanks!
Found 2 solutions by richard1234, robertb:
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Count the numbers in the set {-8000, -7996, -7992, ..., 8000}. Obviously we are not going to do this by hand so what we can do is make transformations to the set by adding 8004 to each element:
|{-8000, -7996, ..., 8000}| = |{4, 8, ..., 16004}| (here |S| denotes the number of elements in set S).
We can divide everything by 4.
|{4, 8, ..., 16004}| = |{1, 2, ..., 4001}|
There are 4001 numbers between -8000 and 8000 inclusive that are divisible by 4.
Answer by robertb(5830)  (Show Source):
You can put this solution on YOUR website! Use the formula for the nth term of an arithmetic series:
==> 8000 = -8000 + (n-1)4 ==> 16000 = 4(n-1)
==> n-1 = 4000 ==> n = 4,001, the number of integers from -8,000 to 8, 000 divisible by 4.
(Note that we have let -8,000 be the first term of the arithmetic series, which is actually divisible by 4.)
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