If each of the following sequences is either arithmetic or geometric, continue the decimal patterns below. a. $$ 0.4,2.3,4.2,6.1 $$. b. $$ 5,2.5,1.25,0.625 $$, Fill in the blanks below. a. $$ 0.4,2.3,4.2,6.1,8.0,9.9 $$, (Type integers or decimals. Simplify your answers.)

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Let's analyze each sequence step by step to determine whether they are arithmetic or geometric, and then continue the patterns.

### Sequence a: $$ 0.4, 2.3, 4.2, 6.1 $$

1. **Identify the pattern**:
   - To check if it's arithmetic, we find the differences between consecutive terms:
     - $$ 2.3 - 0.4 = 1.9 $$
     - $$ 4.2 - 2.3 = 1.9 $$
     - $$ 6.1 - 4.2 = 1.9 $$

Since the difference is constant (1.9), this sequence is arithmetic.

2. **Continue the pattern**:
   - The next term can be found by adding the common difference (1.9) to the last term (6.1):
     - $$ 6.1 + 1.9 = 8.0 $$
   - The term after that:
     - $$ 8.0 + 1.9 = 9.9 $$

Thus, the completed sequence is:
- $$ 0.4, 2.3, 4.2, 6.1, 8.0, 9.9 $$

### Sequence b: $$ 5, 2.5, 1.25, 0.625 $$

1. **Identify the pattern**:
   - To check if it's geometric, we find the ratios between consecutive terms:
     - $$ \frac{2.5}{5} = 0.5 $$
     - $$ \frac{1.25}{2.5} = 0.5 $$
     - $$ \frac{0.625}{1.25} = 0.5 $$

Since the ratio is constant (0.5), this sequence is geometric.

2. **Continue the pattern**:
   - The next term can be found by multiplying the last term (0.625) by the common ratio (0.5):
     - $$ 0.625 	imes 0.5 = 0.3125 $$
   - The term after that:
     - $$ 0.3125 	imes 0.5 = 0.15625 $$

Thus, the completed sequence is:
- $$ 5, 2.5, 1.25, 0.625, 0.3125, 0.15625 $$

### Final Answers:
- a. $$ 0.4, 2.3, 4.2, 6.1, 8.0, 9.9 $$
- b. $$ 5, 2.5, 1.25, 0.625, 0.3125, 0.15625 $$
a. $$ 0.4, 2.3, 4.2, 6.1, 8.0, 9.9 $$ b. $$ 5, 2.5, 1.25, 0.625, 0.3125, 0.15625 $$

If each of the following sequences is either arithmetic or geometric, continue the decimal patterns below. a. \( 0.4,2.3,4.2,6.1 \). b. \( 5,2.5,1.25,0.625 \), Fill in the blanks below. a. \( 0.4,2.3,4.2,6.1,8.0,9.9 \), (Type integers or decimals. Simplify your answers.)

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