Question

Which of the following is an arithmetic sequence? 2, 4, 8, 16, ... -8, -6, -4, -2, ... -2, 4, -6, 8, ...

Answer 1

Given:

Three sequences

2, 4, 8, 16, ...

- 8, - 6, - 4, - 2, ...

- 2, 4, - 6, 8, ...

To find:

Which of the above three sequences, is an arithmetic sequence

Step-by-step explanation:

The first sequence is 2, 4, 8, 16, ...

• Here, second term - first term = 4 - 2 = 2
• and third term - second term = 8 - 4 = 4

Since the differences of the terms are not equal, then the sequence is not an arithmetic sequence.

The second sequence is - 8, - 6, - 4, - 2, ...

• Here, second term - first term = - 6 - (- 8) = - 6 + 8 = 2
• and third term - second term = - 4 - (- 6) = - 4 + 6 = 2.
• Also, fourth term - third term = - 2 - (- 4) = - 2 + 4 = 2.

Since the differences of the terms are equal, then we have a common difference.

Thus this is an arithmetic sequence.

The third sequence is - 2, 4, - 6, 8, ...

• Here, second term - first term = 4 - (- 2) = 4 + 2 = 6
• and third term - second term = - 6 - 4 = - 10.

Since the differences of the terms are not equal, then the sequence is not an arithmetic sequence.

Final Answer:

- 8, - 6, - 4, - 2, ... is an arithmetic sequence.