64,94,144,216

Question

is this arithmetic geometric or neither

Answer 1

To determine whether the sequence 64, 94, 144, 216 is arithmetic, geometric, or neither, we can analyze the differences and ratios.

1. Check for an arithmetic sequence: In an arithmetic sequence, the difference between consecutive terms is constant.

   • 94 - 64 = 30
   • 144 - 94 = 50
   • 216 - 144 = 72

   The differences are: 30, 50, and 72, which are not constant. Therefore, this sequence is not arithmetic.

2. Check for a geometric sequence: In a geometric sequence, the ratio between consecutive terms is constant.

   • 94 / 64 = 1.46875
   • 144 / 94 = 1.531914 ...
   • 216 / 144 = 1.5

   The ratios are not constant either. So, this sequence is not geometric.

Since the sequence is neither arithmetic nor geometric, the final conclusion is that it is neither.