which of the following is an arithmetic sequence?

A. 2,4,8,16,32...
B.-2,-4,-8,16,32...
C.3,6,9,12,15
D.all of the above

1 answer

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Let's analyze the options:

A. \(2, 4, 8, 16, 32...\)

  • The differences between consecutive terms are: \(4 - 2 = 2\), \(8 - 4 = 4\), \(16 - 8 = 8\), \(32 - 16 = 16\).
  • The differences are not constant. Therefore, this is not an arithmetic sequence.

B. \(-2, -4, -8, 16, 32...\)

  • The differences are: \(-4 - (-2) = -2\), \(-8 - (-4) = -4\), \(16 - (-8) = 24\), \(32 - 16 = 16\).
  • The differences are not constant. Therefore, this is not an arithmetic sequence.

C. \(3, 6, 9, 12, 15\)

  • The differences are: \(6 - 3 = 3\), \(9 - 6 = 3\), \(12 - 9 = 3\), \(15 - 12 = 3\).
  • The differences are constant (equal to 3). Therefore, this is an arithmetic sequence.

Given the analysis, the correct answer is: C. \(3, 6, 9, 12, 15\)