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Determine whether the following sequences 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. -12, -10.8, -9.6, -8.4
5. -1, 1, -1, 1

Answer :

A. 98.3, 94.1, 89.9, 85.7 - Arithmetic sequence

B. 1, 0, -1, 0 - Neither

C. 1.75, 3.5, 7, 14 - Geometric sequence

D. -12, -10.8, -9.6, -8.4 - Neither

E. -1, 1, -1, 1 - Neither

We have,

To determine whether each sequence is arithmetic, geometric, or neither, let's examine the differences or ratios between consecutive terms.

98.3, 94.1, 89.9, 85.7

Difference between consecutive terms:

94.1 - 98.3 = -4.2

89.9 - 94.1 = -4.2

85.7 - 89.9 = -4.2

The differences are all -4.2, which means it is an arithmetic sequence.

1, 0, -1, 0

Difference between consecutive terms:

0 - 1 = -1

-1 - 0 = -1

0 - (-1) = 1

The differences are not constant, and it doesn't form a geometric sequence either since the ratio between terms is not constant.

Thus, it is neither arithmetic nor geometric.

1.75, 3.5, 7, 14

The ratio between consecutive terms:

3.5 / 1.75 = 2

7 / 3.5 = 2

14 / 7 = 2

The ratios are all 2, which means it is a geometric sequence.

-12, -10.8, -9.6, -8.4

The ratio between consecutive terms:

-10.8 / -12 ≈ 0.9

-9.6 / -10.8 ≈ 0.888...

-8.4 / -9.6 ≈ 0.875

The ratios are not constant, and it doesn't form an arithmetic sequence either since the differences are not constant.

Thus, it is neither arithmetic nor geometric.

-1, 1, -1, 1

Difference between consecutive terms:

1 - (-1) = 2

-1 - 1 = -2

1 - (-1) = 2

The differences are not constant, and it doesn't form a geometric sequence either since the ratio between terms is not constant.

Thus, it is neither arithmetic nor geometric.

Thus,

A. 98.3, 94.1, 89.9, 85.7 - Arithmetic sequence

B. 1, 0, -1, 0 - Neither

C. 1.75, 3.5, 7, 14 - Geometric sequence

D. -12, -10.8, -9.6, -8.4 - Neither

E. -1, 1, -1, 1 - Neither

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