Question

Select the correct answer.
Observe the sequences below.

I. -3, 1, 5, 9, . . .
II. 1, 2, 4, 8, . . .
III. 4, -12, 36, -108, . . .
IV. 7, 14, 21, 28, . . .

Which of these are arithmetic sequences?

A.
IV only
B.
I, II, and IV
C.
I and IV
D.
II and III

Answer 1

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Let's analyze each sequence:

I. **-3, 1, 5, 9...**
- Difference: \( 1 - (-3) = 4 \), \( 5 - 1 = 4 \), \( 9 - 5 = 4 \)
- This sequence has a constant difference of 4, so it is an arithmetic sequence.

II. **1, 2, 4, 8...**
- Differences: \( 2 - 1 = 1 \), \( 4 - 2 = 2 \), \( 8 - 4 = 4 \)
- The differences are not constant, so this is not an arithmetic sequence.

III. **4, -12, 36, -108...**
- Differences: \( -12 - 4 = -16 \), \( 36 - (-12) = 48 \), \( -108 - 36 = -144 \)
- The differences are not constant, so this is not an arithmetic sequence.

IV. **7, 14, 21, 28...**
- Difference: \( 14 - 7 = 7 \), \( 21 - 14 = 7 \), \( 28 - 21 = 7 \)
- This sequence has a constant difference of 7, so it is an arithmetic sequence.

Now, we can summarize the findings:
- **I**: Arithmetic sequence
- **II**: Not an arithmetic sequence
- **III**: Not an arithmetic sequence
- **IV**: Arithmetic sequence

The arithmetic sequences are I and IV.

Thus, the correct answer is **C. I and IV**.