Question

The recursive rule for a sequence is f(n)= f(n-1) / 2 + 5. The first term is 4. What is the third term?

a. 3

b. 4.5

c. 7.25

d. 11.625

Answer 1

To find the third term of the sequence defined by the recursive rule f(n) = f(n-1) / 2 + 5 with the first term 4, we calculate the terms sequentially. The second term is 7 and the third term is 8.5, which is not among the provided options.

Step-by-step explanation:

To find the third term of the sequence defined by the recursive rule f(n) = f(n-1) / 2 + 5, where the first term is 4, we need to first determine the second term and then use it to calculate the third one.

1. For n=2: f(2) = f(2-1) / 2 + 5 = f(1) / 2 + 5. Since the first term f(1) is 4, it follows that f(2) = 4 / 2 + 5 = 2 + 5 = 7.
2. For n=3: f(3) = f(3-1) / 2 + 5 = f(2) / 2 + 5. Using the second term we just found, f(3) = 7 / 2 + 5 = 3.5 + 5 = 8.5.

However, none of the options match 8.5. If we are to find the third term according to the recursive formula given, with the first term being 4, the correct answer should be 8.5, not any of the provided options (a) 3, (b) 4.5, (c) 7.25, or (d) 11.625.