 # Which of the following sequences is NOT arithmetic?(A) -4, 2, 8, 14, ..., (B) 9, 4, -1, -6, ... (C) 2, 4, 8, 16,... (D)frac{1}{3},1*frac{1}{3},2*frac{1}{3},3*frac{1}{3}',... Sinead Mcgee 2021-01-10 Answered

Which of the following sequences is NOT arithmetic?
(A) -4, 2, 8, 14, ...,
(B) 9, 4, -1, -6, ...
(C) 2, 4, 8, 16,...
(D)',...

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An arithmetic sequence contain a constant common difference between each term. To find the common difference, we can subtract the first term from the second term. Doing this, we found that only C does not have a constant common difference, hence making it not an arithmetic sequence.
Let d = common difference
A) $14-8=6$
$8-2=6$
$2-\left(-4\right)=6$
$d=6$
B) $-6-\left(-1\right)=-5$
$-1-4=-5$
$4-9=-5$
$d=-5$
C) $16-8=8$
$8-4=4$
$4-2=2$
d=does not exist
D) $3×\frac{1}{3}-2×\frac{1}{3}=1$
$2×\frac{1}{3}-1×\frac{1}{3}=1$
$1×\frac{1}{3}-\frac{1}{3}=1$
$d=1$
Result: Choice C