Identify the sequences as arithmetic, geometric, or neither.(3 points)

Question

Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
-5, -2, 1, 4, 7, . . .
2, 6, 18, 54,162, . . .
1, 20, 2, 40, 3, 60, . . .

Answer 1

Let's analyze each sequence:

1. -5, -2, 1, 4, 7, ...

   • To check if it's arithmetic, we find the differences between consecutive terms:
     • (-2) - (-5) = 3
     • 1 - (-2) = 3
     • 4 - 1 = 3
     • 7 - 4 = 3
   • The common difference is 3. Therefore, this sequence is arithmetic.

2. 2, 6, 18, 54, 162, ...

   • To check if it's geometric, we find the ratios between consecutive terms:
     • 6 / 2 = 3
     • 18 / 6 = 3
     • 54 / 18 = 3
     • 162 / 54 = 3
   • The common ratio is 3. Therefore, this sequence is geometric.

3. 1, 20, 2, 40, 3, 60, ...

   • For this sequence, it doesn't follow a consistent additive or multiplicative pattern:
     • The sequence alternates between numbers and appears to multiply or modify in a non-linear fashion.
   • Therefore, this sequence is neither.

In summary:

1. Arithmetic
2. Geometric
3. Neither