SOLUTION: How many integers from -8000 to 8000 are divisible by 4? Please explain how I could approach and solve this, thanks!

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.)
RELATED QUESTIONS
I figured out the answer but I am clueless as to the equation. Can you please help????... (answered by stanbon)
Hi. Can someone please teach me how to solve this question? It's quite easy but I want to (answered by KMST)
Hi. Can someone please teach me how to solve this question? It's quite easy but I want to (answered by math-vortex,AnlytcPhil)
Can you help me with this question please? How many years will it take $5000 to grow... (answered by jim_thompson5910)
Patti needs 8000 litres of a 35% solution of hydrogen chloride. How many litres of a 40%... (answered by rajagopalan)
Ok I am still struggling with what I am doing wrong. The problem is $8000 for 10 years... (answered by gonzo)
After j candies were given to k kids, each kid has the same number of candies, with four... (answered by richard1234)
James has two malfunctioning robots. One of theme beeps every 4 seconds; the other beeps... (answered by Edwin McCravy)
When a positive integer n is divided by 6, the remainder is 2. What is the remainder when (answered by richard1234)