Question

Which sequence is generated by the function f(n + 1) = f(n) - 2 for f(1) = 10?

A) 0, -10, -12, -14, -16, -18, ...
B) -2, -8, 18, 28, 38, ...
C) 8, 18, 28, 38, 48, ...
D) 10, 8, 6, 4, 2, ...

Answer 1

The sequence generated by the function f(n + 1) = f(n) - 2 for f(1) = 10 is represented by option A) 0, -10, -12, -14, -16, -18, ...

Step-by-step explanation:

The sequence generated by the function f(n + 1) = f(n) - 2 for f(1) = 10 is represented by option A) 0, -10, -12, -14, -16, -18, ...

To find the sequence, we can start with the given value f(1) = 10 and repeatedly apply the function to find the next terms in the sequence. Here's how we can do it:

1. Start with the given term f(1) = 10
2. Apply the function: f(2) = f(1) - 2 = 10 - 2 = 8
3. Apply the function again: f(3) = f(2) - 2 = 8 - 2 = 6
4. Continue applying the function to find the rest of the terms in the sequence: f(4) = 6 - 2 = 4, f(5) = 4 - 2 = 2, f(6) = 2 - 2 = 0, f(7) = 0 - 2 = -2, f(8) = -2 - 2 = -4, ...

Therefore, the sequence generated by the given function is 0, -10, -12, -14, -16, -18, ...