Which is an arithmetic sequence?
A. 1, 4, 9, 16, . . .
B. 2, 1, –1, –4, . . .
C. 4, 8, 16, 32, . . .
D. 21, 9, –3, –15, . . .
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help please
an arithmetic sequence has a constant difference between terms. Looking at the differences, we see:
A. 3,5,7, . . .
B. -1,-2,-3, . . .
C. 4,8,16, . . .
D. -12,-12,-12, . . .
I guess the answer is D, eh?
To determine which of the given sequences is an arithmetic sequence, we need to check if there is a common difference between consecutive terms.
Let's analyze each sequence:
A. 1, 4, 9, 16, ...
To find the difference between consecutive terms, we subtract each term from the one before it:
4 - 1 = 3
9 - 4 = 5
16 - 9 = 7
Since the differences are not the same, this sequence is not arithmetic.
B. 2, 1, -1, -4, ...
Using the same method:
1 - 2 = -1
-1 - 1 = -2
-4 - (-1) = -3
Again, the differences are not consistent, so this sequence is not arithmetic.
C. 4, 8, 16, 32, ...
Calculating the differences:
8 - 4 = 4
16 - 8 = 8
32 - 16 = 16
In this case, each term is obtained by multiplying the previous term by 2, so this sequence is geometric, not arithmetic.
D. 21, 9, -3, -15, ...
Computing the differences:
9 - 21 = -12
-3 - 9 = -12
-15 - (-3) = -12
The differences are consistent (-12 in this case), so this sequence is arithmetic.
To summarize, the arithmetic sequence is:
D. 21, 9, -3, -15, ...
I hope this explanation helps! Let me know if you have any further questions.