identifying arithmetic sequences

Question

-4,-2,0,2,...

Answer 1

This is a little confusing especially when you involve negative numbers and positive numbers in the same sequence.  When identifying a numerical sequence you need to take a deep breathe and attempt to find the simpliest solution.

-4,-2,0,2...

how to get to -2

-4+2= -2, -2+2=0, 0+2=2 ... 

or you can say

2 + (-4) = -2   You are just adding specific values to the number in the sequence to find the next given number.

you could say -4 + 2x, when x is all positive Whole numbers starting at 1.  Or -4 + 2(x+1) if you want to have x start at 0.  But if your like me you will want to keep it simple just start at 1 hahaha. Hope this helps.

Answer 2

When identifying arithmetic sequences look for a pattern. If you can't determine the pattern right away just focus on two numbers. Think of many different ways you can calculate from one number to the next. Then see if you can apply the same rule to the other numbers in the sequence. 

For example: 

To get from -4 to -2 

-4 x 1/2 = -2 

-4 + 2 = -2 

-4 ÷ 2 = -2 

-4 - (-2) = -2

So you can see that there are multiple ways to get from -4 to -2. 

Try to apply each of these rules to the other numbers . 

-2 to 0 

-2 x 1/2 = -1

-2 + 2 = 0

-2 ÷ 2 = -1

-2 - (-2) = 0

Now you can see that only adding 2 or subtracting -2 gets you the third term. Continue these with the other numbers to see which way works for every term