which arithmetic sequence is described by the linear function f (n) = 1/2n -13
A -13, -25/2 -12
B 27/2 14 29/2
C -25/2 -23/2 -21/2
D -25/2 -12 -23/2
The common difference in an arithmetic sequence is represented by the coefficient of n in the linear function.
f(n) = 1/2n - 13
So, the common difference is 1/2.
Looking at the answer choices:
A) -13, -25/2, -12 --> Common difference = -25/2 - (-13) = -12 - (-25/2) = -12 + 25/2 = 1/2 --> This is the correct arithmetic sequence.
B) 27/2, 14, 29/2 --> Common difference = 14 - 27/2 = 29/2 - 14 = 1/2, the common difference is 1/2.
C) -25/2, -23/2, -21/2 --> Common difference = -23/2 - (-25/2) = -21/2 - (-23/2) = 1/2, the common difference is 1/2.
D) -25/2, -12, -23/2 --> Common difference = -12 - (-25/2) = -23/2 - (-12) = 1/2, the common difference is 1/2.
Therefore, the arithmetic sequence described by the linear function f(n) = 1/2n - 13 is A: -13, -25/2, -12.