Questions: Question 2 33 pts Which of the following sequences is arithmetic sequence: 1, 100, 1000, 10000, ... -3, 1, 5, 9, ... 0, 0.1, 0.2, 0.3, 0.4, 0.5, ... 1, 2, 4, 8, 16, 32, ... -3, -11, -19, -26, ...

Solution Steps

To determine if a sequence is arithmetic, we need to check if the difference between consecutive terms is constant. We will calculate the differences between consecutive terms for each sequence and verify if they are the same throughout the sequence.

We are given the following sequences to analyze for arithmetic properties:

1. \(1, 100, 1000, 10000\)
2. \(-3, 1, 5, 9\)
3. \(0, 0.1, 0.2, 0.3, 0.4, 0.5\)
4. \(1, 2, 4, 8, 16, 32\)
5. \(-3, -11, -19, -26\)

We will calculate the differences between consecutive terms for each sequence:

1. For \(1, 100, 1000, 10000\):

   • Differences: \(100 - 1 = 99\), \(1000 - 100 = 900\), \(10000 - 1000 = 9000\) (not constant)

2. For \(-3, 1, 5, 9\):

   • Differences: \(1 - (-3) = 4\), \(5 - 1 = 4\), \(9 - 5 = 4\) (constant)

3. For \(0, 0.1, 0.2, 0.3, 0.4, 0.5\):

   • Differences: \(0.1 - 0 = 0.1\), \(0.2 - 0.1 = 0.1\), \(0.3 - 0.2 = 0.1\), \(0.4 - 0.3 = 0.1\), \(0.5 - 0.4 = 0.1\) (constant)

4. For \(1, 2, 4, 8, 16, 32\):

   • Differences: \(2 - 1 = 1\), \(4 - 2 = 2\), \(8 - 4 = 4\), \(16 - 8 = 8\), \(32 - 16 = 16\) (not constant)

5. For \(-3, -11, -19, -26\):

   • Differences: \(-11 - (-3) = -8\), \(-19 - (-11) = -8\), \(-26 - (-19) = -7\) (not constant)

From the calculations:

• Sequence 1: Not arithmetic
• Sequence 2: Arithmetic (common difference = 4)
• Sequence 3: Arithmetic (common difference = 0.1)
• Sequence 4: Not arithmetic
• Sequence 5: Not arithmetic

Final Answer