Answer :
Let's analyze the sequences one by one to determine if they are arithmetic, geometric, or neither:
1. Sequence 1: [tex]\(98.3, 94.1, 89.9, 85.7, \ldots\)[/tex]
- Arithmetic Sequences have a constant difference between consecutive terms.
- Here, [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 difference is constant, this sequence is Arithmetic.
2. Sequence 2: [tex]\(1, 0, -1, 0, \ldots\)[/tex]
- This sequence fluctuates between 1, 0, -1, and back to 0.
- Arithmetic Sequences have constant differences, and Geometric Sequences have constant ratios.
- The fluctuation means neither a constant difference nor a constant ratio is present.
- This sequence is Neither.
3. Sequence 3: [tex]\(1.75, 3.5, 7, 14\)[/tex]
- Geometric Sequences have a constant ratio between consecutive terms.
- Here, [tex]\(3.5 / 1.75 = 2\)[/tex], [tex]\(7 / 3.5 = 2\)[/tex], [tex]\(14 / 7 = 2\)[/tex].
- Since the ratio is constant, this sequence is Geometric.
4. Sequence 4: [tex]\(-12, -10.8, -9.6, -8.4\)[/tex]
- Check for an Arithmetic Sequence by looking for a constant difference.
- Here, [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 difference is constant, this sequence is Arithmetic.
5. Sequence 5: [tex]\(-1, 1, -1, 1, \ldots\)[/tex]
- Similar to Sequence 2, this pattern switches between -1 and 1.
- There is no consistent pattern for an Arithmetic Sequence (constant difference) or Geometric Sequence (constant ratio).
- This sequence is Neither.
In summary:
- Sequence 1 is Arithmetic.
- Sequence 2 is Neither.
- Sequence 3 is Geometric.
- Sequence 4 is Arithmetic.
- Sequence 5 is Neither.
1. Sequence 1: [tex]\(98.3, 94.1, 89.9, 85.7, \ldots\)[/tex]
- Arithmetic Sequences have a constant difference between consecutive terms.
- Here, [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 difference is constant, this sequence is Arithmetic.
2. Sequence 2: [tex]\(1, 0, -1, 0, \ldots\)[/tex]
- This sequence fluctuates between 1, 0, -1, and back to 0.
- Arithmetic Sequences have constant differences, and Geometric Sequences have constant ratios.
- The fluctuation means neither a constant difference nor a constant ratio is present.
- This sequence is Neither.
3. Sequence 3: [tex]\(1.75, 3.5, 7, 14\)[/tex]
- Geometric Sequences have a constant ratio between consecutive terms.
- Here, [tex]\(3.5 / 1.75 = 2\)[/tex], [tex]\(7 / 3.5 = 2\)[/tex], [tex]\(14 / 7 = 2\)[/tex].
- Since the ratio is constant, this sequence is Geometric.
4. Sequence 4: [tex]\(-12, -10.8, -9.6, -8.4\)[/tex]
- Check for an Arithmetic Sequence by looking for a constant difference.
- Here, [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 difference is constant, this sequence is Arithmetic.
5. Sequence 5: [tex]\(-1, 1, -1, 1, \ldots\)[/tex]
- Similar to Sequence 2, this pattern switches between -1 and 1.
- There is no consistent pattern for an Arithmetic Sequence (constant difference) or Geometric Sequence (constant ratio).
- This sequence is Neither.
In summary:
- Sequence 1 is Arithmetic.
- Sequence 2 is Neither.
- Sequence 3 is Geometric.
- Sequence 4 is Arithmetic.
- Sequence 5 is Neither.
