Question

For each of the following sequences, is the common difference equal to 5?

A. f(n) = 5n - 3
B. f(n) = -2n
C. f(n) = 4n - 1

Answer 1

Only the sequence represented by the function f(n) = 5n - 3 has a common difference of 5. The other functions, f(n) = -2n and f(n) = 4n - 1, do not have a common difference of 5.

Step-by-step explanation:

The question asks whether the common difference in the given sequences is equal to 5. Let's analyze each function by finding the difference between consecutive terms:

1. f(n) = 5n - 3: Using two consecutive terms, f(2) = 5(2) - 3 = 7 and f(1) = 5(1) - 3 = 2. The difference, f(2) - f(1), is 7 - 2 = 5, so the common difference here is indeed 5.
2. f(n) = -2n: Similarly, f(2) = -2(2) = -4 and f(1) = -2(1) = -2. The difference, f(2) - f(1), is -4 - (-2) = -2, which is not 5. Thus, the common difference is not 5.
3. f(n) = 4n - 1: Using consecutive terms again, f(2) = 4(2) - 1 = 7 and f(1) = 4(1) - 1 = 3. The difference, f(2) - f(1), is 7 - 3 = 4, so the common difference is not 5.

Only the sequence represented by the function f(n) = 5n - 3 has a common difference of 5.