Question

Consider the sequence of numbers: 3/8, 3/4, 1 1/8, 1 1/2, 1 7/8. Which statement is a description of the sequence?

a) The sequence is recursive, where each term is 1/4 greater than its preceding term.
b) The sequence is recursive and can be represented by the function f(n + 1) = f(n) + f(n + 1/8).
c) The sequence is arithmetic, where each pair of terms has a constant difference of 3/4.
d) The sequence is arithmetic and can be represented by the function f(n + 1) = f(n) + (3/8).

Answer 1

The sequence is arithmetic, where each pair of terms has a constant difference of 3/4.

Step-by-step explanation:

The sequence described in the question is arithmetic. Each pair of terms has a constant difference of 3/8. To determine this, let's subtract each term from its preceding term:

3/4 - 3/8 = 3/8

1 1/8 - 3/4 = 3/8

1 1/2 - 1 1/8 = 3/8

1 7/8 - 1 1/2 = 3/8

Since the difference between each pair of terms is always 3/8, we can conclude that the sequence is arithmetic.

The correct statement that describes the sequence is option c) The sequence is arithmetic, where each pair of terms has a constant difference of 3/4.