Question

Which of the following sequences represents an arithmetic sequence?



-7, -4, 1, 4, ...

2, -4, 8, -16, ...

1, 4, 9, 16, ...

-5, -3, -1, 1, ...

Answer 1

Arithmetic is strictly increasing or decreasing in a constant amount.

Answer 2

In an arithmetic sequence, the difference between any two consecutive terms is the same.

Answer 3

There is only one pattern that is like that. The others have inconsistent intervals.

Answer 4

-7,-4, 1, and 4 change from

3, 6, 3 in the spaces between the intervals.

Does this make sense to you?

-5,-3,-1, and 1 all have consistent intervals of 2

Answer 5

That means, subtract the first term from the second term. Subtract the second term from the third term. Subtract the third term from the fourth term, and so on.. If all the subtractions give you the same result, it's an arithmetic sequence.

Answer 6

Let's look at the first sequence: -7, -4, 1, 4, ...

-4 - (-7) = 3
1 - (-4) = 5
Since you already have two different results, this cannot be an arithmetic sequence.

Now check out the second sequence the same way.