SOLUTION: how many multiples of 3 are between -3002 to 6001?

Question 880498: how many multiples of 3 are between -3002 to 6001?
Found 2 solutions by josmiceli, richwmiller:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
If you start with , the next
HIGHER number divisible by is

----------------
The next LOWER number less than
that is divisible by is
---------------
So, the column of numbers between these
( an including these ) that is divisible by
looks like:
-3000
-3000 + 3
-3000 + 6
-3000 + 9
All the way up to
-3000 + 9000
---------------------
Each of the entries also looks like:
-3000 + 3*0
-3000 + 3*1
-3000 + 3*2
All the way up to
-3000 + 3*3000
-------------------
So, it looks like to get to the final entry
you have multipliers ( 0 - 3000 )
of added to
----------------------
So, there are 3001 multiples of 3 between
-3002 and 6001
-
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
An = A1 + (n - 1)d
6000=-3000+3(n-1)
2000=-1000+n-1
3001=n
6000 is the 3001th term starting with -3000

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