High School

Sort the sequences based on whether they are arithmetic, geometric, or neither.

1) 98.3, 94.1, 89.9, 85.7
2) 1, 0, -1, 0
3) 1.75, 3.5, 7, 14
4) -1, 1, -1, 1
5) -12, -10.8, -9.6, -8.4

Answer :

her answer is right but you just have to switch 4 and 5 around 4 is geometric while 5 is arithmetic

Final Answer:

Each sequence is tested for a common difference or ratio to determine if it is arithmetic or geometric. The sequences 98.3, 94.1, 89.9, 85.7 and -12, -10.8, -9.6, -8.4 are arithmetic, 1.75, 3.5, 7, 14 is geometric, and 1, 0, -1, 0 as well as -1, 1, -1, 1 are neither.

Explanation:

To determine if a sequence is arithmetic, geometric, or neither, we look for a common difference or ratio between consecutive terms.

  1. For the sequence 98.3, 94.1, 89.9, 85.7, we subtract consecutive terms: 94.1 - 98.3 = -4.2, 89.9 - 94.1 = -4.2, 85.7 - 89.9 = -4.2. The common difference is -4.2, so this sequence is arithmetic.
  2. The sequence 1, 0, -1, 0 does not have a common difference or ratio, so it is neither arithmetic nor geometric.
  3. For 1.75, 3.5, 7, 14, the ratios are 3.5/1.75 = 2, 7/3.5 = 2, and 14/7 = 2. The common ratio is 2, so this sequence is geometric.
  4. The sequence -1, 1, -1, 1 alternates signs without a common difference or ratio, so it is neither.
  5. For the sequence -12, -10.8, -9.6, -8.4, the difference is -10.8 - (-12) = 1.2, -9.6 - (-10.8) = 1.2, -8.4 - (-9.6) = 1.2. The common difference is 1.2, making it an arithmetic sequence.

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