Question

Determine if each sequence is arithmetic, geometric, or neither.

Answer 1

9514 1404 393

Answer:

• geometric
• arithmetic
• neither (Fibonacci sequence)

Step-by-step explanation:

If ratios are the same, it is geometric:

  8/4 = 16/8 = ... = 2

If differences are the same, it is arithmetic:

  -4-(-8) = 0 -(-4) = ... = 4

If neither is the case, it is neither:

  3-2 ≠ 5 -3

  3/2 ≠ 5/3

In this last sequence we see that differences equal the previous term. This is characteristic of the Fibonacci sequence, which sees wide use in Nature, and has a relationship to the Golden Ratio. (The ratios of successive terms approach the golden ratio (1+√5)/2 ≈ 1.618.)