Answer :
Let's determine whether each sequence is arithmetic, geometric, or neither by checking their patterns.
1. Sequence: [tex]\( 98.3, 94.1, 89.9, 85.7, \ldots \)[/tex]
- To check if it's arithmetic, we calculate the common difference.
- [tex]\( 94.1 - 98.3 = -4.2 \)[/tex]
- [tex]\( 89.9 - 94.1 = -4.2 \)[/tex]
- [tex]\( 85.7 - 89.9 = -4.2 \)[/tex]
Since the differences are the same, this sequence is Arithmetic.
2. Sequence: [tex]\( 1, 0, -1, 0, \ldots \)[/tex]
- This sequence alternates between 1 and 0, and then -1, repeating the pattern.
- It doesn't have a constant difference (arithmetic) nor a constant ratio (geometric).
This sequence is Neither.
3. Sequence: [tex]\( 1.75, 3.5, 7, 14 \)[/tex]
- To check if it's geometric, we calculate the common ratio.
- [tex]\( 3.5 \div 1.75 = 2 \)[/tex]
- [tex]\( 7 \div 3.5 = 2 \)[/tex]
- [tex]\( 14 \div 7 = 2 \)[/tex]
Since the ratios are the same, this sequence is Geometric.
4. Sequence: [tex]\( -12, -10.8, -9.6, -8.4 \)[/tex]
- To check if it's arithmetic, we calculate the common difference.
- [tex]\( -10.8 - (-12) = 1.2 \)[/tex]
- [tex]\( -9.6 - (-10.8) = 1.2 \)[/tex]
- [tex]\( -8.4 - (-9.6) = 1.2 \)[/tex]
Since the differences are the same, this sequence is Arithmetic.
5. Sequence: [tex]\( -1, 1, -1, 1, \ldots \)[/tex]
- This sequence alternates between -1 and 1.
- It doesn't have a constant difference (arithmetic) nor a constant ratio (geometric).
This sequence is Neither.
Summary:
- [tex]\( 98.3, 94.1, 89.9, 85.7, \ldots \)[/tex] is Arithmetic
- [tex]\( 1, 0, -1, 0, \ldots \)[/tex] is Neither
- [tex]\( 1.75, 3.5, 7, 14 \)[/tex] is Geometric
- [tex]\( -12, -10.8, -9.6, -8.4 \)[/tex] is Arithmetic
- [tex]\( -1, 1, -1, 1, \ldots \)[/tex] is Neither
1. Sequence: [tex]\( 98.3, 94.1, 89.9, 85.7, \ldots \)[/tex]
- To check if it's arithmetic, we calculate the common difference.
- [tex]\( 94.1 - 98.3 = -4.2 \)[/tex]
- [tex]\( 89.9 - 94.1 = -4.2 \)[/tex]
- [tex]\( 85.7 - 89.9 = -4.2 \)[/tex]
Since the differences are the same, this sequence is Arithmetic.
2. Sequence: [tex]\( 1, 0, -1, 0, \ldots \)[/tex]
- This sequence alternates between 1 and 0, and then -1, repeating the pattern.
- It doesn't have a constant difference (arithmetic) nor a constant ratio (geometric).
This sequence is Neither.
3. Sequence: [tex]\( 1.75, 3.5, 7, 14 \)[/tex]
- To check if it's geometric, we calculate the common ratio.
- [tex]\( 3.5 \div 1.75 = 2 \)[/tex]
- [tex]\( 7 \div 3.5 = 2 \)[/tex]
- [tex]\( 14 \div 7 = 2 \)[/tex]
Since the ratios are the same, this sequence is Geometric.
4. Sequence: [tex]\( -12, -10.8, -9.6, -8.4 \)[/tex]
- To check if it's arithmetic, we calculate the common difference.
- [tex]\( -10.8 - (-12) = 1.2 \)[/tex]
- [tex]\( -9.6 - (-10.8) = 1.2 \)[/tex]
- [tex]\( -8.4 - (-9.6) = 1.2 \)[/tex]
Since the differences are the same, this sequence is Arithmetic.
5. Sequence: [tex]\( -1, 1, -1, 1, \ldots \)[/tex]
- This sequence alternates between -1 and 1.
- It doesn't have a constant difference (arithmetic) nor a constant ratio (geometric).
This sequence is Neither.
Summary:
- [tex]\( 98.3, 94.1, 89.9, 85.7, \ldots \)[/tex] is Arithmetic
- [tex]\( 1, 0, -1, 0, \ldots \)[/tex] is Neither
- [tex]\( 1.75, 3.5, 7, 14 \)[/tex] is Geometric
- [tex]\( -12, -10.8, -9.6, -8.4 \)[/tex] is Arithmetic
- [tex]\( -1, 1, -1, 1, \ldots \)[/tex] is Neither
