Question 1083614: What is the common difference, d of the sequence shown below?
-1, -5, -9, -13, -17, -21, …
A) 4
B) -4
C) -1
D) -5
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Answer: Choice B) -4
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Explanation:
Pick any term but the first one. Whatever term you picked, subtract off the previous term
Let's say you picked the third term -9. The previous term is -5. Subtract these values:
(term picked) - (previous term) = (-9) - (-5)
(term picked) - (previous term) = -9 + 5
(term picked) - (previous term) = -4
which is the common difference.
Let's try another selection. Pick the fifth term -17
The previous term is -13
(term picked) - (previous term) = (-17) - (-13)
(term picked) - (previous term) = -17 + 13
(term picked) - (previous term) = -4
we get the same result. This will happen with any selection you make. You can't pick on the first term because there's no known terms before it.
Note how each term is decreasing by 4 each time. This is another way to see that the common difference is -4
As you can see
second term = (first term) + (common difference) = -1 + (-4) = -5
third term = (second term) + (common difference) = -5 + (-4) = -9
fourth term = (third term) + (common difference) = -9 + (-4) = -13
fifth term = (fourth term) + (common difference) = -13 + (-4) = -17
and so on...
Answer by MathLover1(20850)  (Show Source):
You can put this solution on YOUR website!
Given an arithmetic series
 ,  ,  , ..., the number  is called the common difference associated to the sequence
 , ,  ,  ,  ,  , …
the common difference is 
check:
 ...and so on
answer is: B) 
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