Question

A sequence is defined by the formula LaTeX: f(n+1)=f(n)-50f ( n + 1 ) = f ( n ) − 50and LaTeX: f(1)=100f ( 1 ) = 100. What is LaTeX: f(4)f ( 4 )?

Answer 1

To calculate f(4) in the given recursive sequence, we sequentially apply the formula, subtracting 50 from the previous term. Starting with f(1) = 100, the fourth term, f(4), is calculated as -50.

Step-by-step explanation:

The student has provided a recursive sequence where each term is found by subtracting 50 from the previous term, with the starting value given as f(1) = 100. To find f(4), we will apply the same rule three more times:

1. f(2) = f(1) - 50 = 100 - 50 = 50
2. f(3) = f(2) - 50 = 50 - 50 = 0
3. f(4) = f(3) - 50 = 0 - 50 = -50

Therefore, the fourth term in the sequence, f(4), is -5