Which of the following statements correctly determines the rule for generating the next term in the sequence 23, 19.5, 16, 12.5....(1 point)

Responses

Multiply by the common ration of -3.5
Multiply by the common ration of -3.5

Add the common ratio of -3.5
Add the common ratio of -3.5

Multiply by the common difference of -3.5
Multiply by the common difference of -3.5

Add the common difference of -3.5

1 answer

To determine the next term in the sequence 23, 19.5, 16, 12.5, we can look at the differences between consecutive terms:

  • 23 to 19.5 = 23 - 19.5 = 3.5
  • 19.5 to 16 = 19.5 - 16 = 3.5
  • 16 to 12.5 = 16 - 12.5 = 3.5

The terms are decreasing by 3.5 each time, which indicates that 3.5 is the common difference.

To find the next term, we subtract 3.5 from the last term (12.5): 12.5 - 3.5 = 9.

Based on this analysis, the correct statement is:

Add the common difference of -3.5.

However, since we're subtracting 3.5, you could also think of it as adding the common ratio of -3.5 to yield the next term. But the language in the options focuses on "adding" rather than "subtracting," which is indeed correct for this sequence.

So, the best option is:

Add the common difference of -3.5.