Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 64,8,1,

Question

Please clarify if it is a Geometric or Arithmetic, and can you define the common difference between the numbers????

Answer 1

In an arithmetic sequence, you can subtract any two consecutive terms and get the same value (the common difference).

8 - 64 = -56

1 - 8 = -7

Since -56 and -7 are different values, this is NOT an arithmetic sequence.

In a geometric sequence, you can divide any two consecutive terms and get the same value (the common ratio).

8/64 = 0.125 (or 1/8)

1/8 = 0.125 (or 1/8)

Since these are the same values, this IS a geometric sequence and 0.125 (or 1/8) is the common ratio.