Question

Which function describes the sequence 1, 4, 7, 10, 13, ...?

A. (1) = 1, fn - 1) = f(n) + 3 for n
B. 1) = 1, f(n) = f(n - 1) + 3 for n
C. f(1) = 1, r(n + 1) = f(n) - 3 for n
D. f(1) = 1, f(n) = f(n - 1) - 3 for n

Answer 1

A function that starts with the initial value of 1 and adds 3 to get the subsequent terms correctly describes the given sequence as Option B: f(1) = 1, f(n) = f(n - 1) + 3 for n > 1.

Step-by-step explanation:

The given sequence is 1, 4, 7, 10, 13, ..., and we are looking for a function that describes this sequence. The pattern is that each term increases by 3 compared to the previous term. Therefore, the correct function would be the one that starts with an initial value, f(1) = 1, and adds 3 to the previous term to calculate the next term.

The correct answer is Option B: f(1) = 1, f(n) = f(n - 1) + 3 for n > 1. This function correctly starts the sequence at 1 and defines each subsequent term to be 3 greater than the one before it, which matches the given sequence.