Question

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

• $-10, -12, -14, -16, -18, ...$
• $-2, 8, 18, 28, 38, ...$
• $8, 18, 28, 38, 48, ...$
• $10, 8, 6, 4, 2, ...$

Explanation:

Step1: Understand the recursive formula

The function is \( f(n + 1)=f(n)-2 \) with \( f(1) = 10 \). This means each term is 2 less than the previous term.

Step2: Calculate the first few terms

• For \( n = 1 \), \( f(1)=10 \).
• For \( n = 2 \), \( f(2)=f(1)-2=10 - 2=8 \).
• For \( n = 3 \), \( f(3)=f(2)-2=8 - 2 = 6 \).
• For \( n = 4 \), \( f(4)=f(3)-2=6 - 2=4 \).
• For \( n = 5 \), \( f(5)=f(4)-2=4 - 2=2 \).

So the sequence starts with 10, then 8, 6, 4, 2, ...

Answer:

D. 10, 8, 6, 4, 2, ...