Question

Determine which sequence is an arithmetic sequence.

A. –16, –12, –8, –4, . . .
B. 1, 4, 2, 5, 3, . . .
C. 4, 8, 16, 32, . . .
D. 1, 1, 2, 3, 5, . . .

Answer 1

Option A (-16, -12, -8, -4, ...) is the correct arithmetic sequence, with a common difference of 4 between each term.

Step-by-step explanation:

Determine the Arithmetic Sequence

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant, known as the common difference. To identify an arithmetic sequence from the options, we need to check the difference between successive terms:

• Option A: – 16, – 12, – 8, – 4, ...
  Here, each term increases by 4 (– 12 - (– 16) = 4, – 8 - (– 12) = 4, etc.), so this is an arithmetic sequence with a common difference of 4.
• Option B: 1, 4, 2, 5, 3, ...
  The differences are not consistent, so this is not an arithmetic sequence.
• Option C: 4, 8, 16, 32, ...
  This sequence shows a pattern of each term being twice the previous, which characterizes a geometric sequence, not arithmetic.
• Option D: 1, 1, 2, 3, 5, ...
  This resembles the Fibonacci sequence, where each term is the sum of the previous two terms, thus not an arithmetic sequence.

Therefore, the sequence that is an arithmetic sequence is Option A.