To solve this problem, we need to determine the value of [tex]\( f(3) \)[/tex] given the initial term and the recursive function.
We are given:
- The first term of the sequence, [tex]\( f(1) = 10 \)[/tex].
- The recursive formula, [tex]\( f(n+1) = f(n) - 2 \)[/tex].
Let's find the values step by step:
1. Determine [tex]\( f(2) \)[/tex]:
- Using the recursive formula, substitute [tex]\( n = 1 \)[/tex]:
[tex]\[
f(2) = f(1) - 2
\][/tex]
- Since [tex]\( f(1) = 10 \)[/tex]:
[tex]\[
f(2) = 10 - 2 = 8
\][/tex]
2. Determine [tex]\( f(3) \)[/tex]:
- Using the recursive formula, substitute [tex]\( n = 2 \)[/tex]:
[tex]\[
f(3) = f(2) - 2
\][/tex]
- Since [tex]\( f(2) = 8 \)[/tex]:
[tex]\[
f(3) = 8 - 2 = 6
\][/tex]
Therefore, the value of [tex]\( f(3) \)[/tex] is [tex]\( 6 \)[/tex].
The correct answer is:
6
