Question

which of the following statements correctly describes the sequence 4, 5.5, 7, 8.5, …? (1 point)

• it is an arithmetic sequence with a common difference of 1.5.
• it is a geometric sequence with a common difference of 1.5.
• it is an arithmetic sequence with a common ratio of 1.5.
• it is a geometric sequence with a common ratio of 1.5.

Explanation:

1. Recall the definitions: An arithmetic sequence has a common difference (subtracting consecutive terms gives the same value), and a geometric sequence has a common ratio (dividing consecutive terms gives the same value).
2. Check the given sequence \(4, 5.5, 7, 8.5, \dots\):

• Calculate the difference between consecutive terms: \(5.5 - 4 = 1.5\), \(7 - 5.5 = 1.5\), \(8.5 - 7 = 1.5\). So, there is a common difference of \(1.5\), which means it is an arithmetic sequence (not geometric, since the ratio between terms like \(5.5\div4 = 1.375\), \(7\div5.5\approx1.27\) is not constant).
• Eliminate options with incorrect terms: Geometric sequences have a common ratio (not difference), and arithmetic sequences have a common difference (not ratio). So, options with "geometric sequence with a common difference" or "arithmetic sequence with a common ratio" are incorrect.

Answer:

A. It is an arithmetic sequence with a common difference of 1.5.