A sequence is defined by the recursive formula [tex]$f(n+1)=f(n)-2$[/tex]. If [tex]$f(1)=18$[/tex], what is [tex][tex]$f(5)$[/tex][/tex]?



Answer :

To find [tex]\( f(5) \)[/tex] for the sequence defined by the recursive formula [tex]\( f(n+1) = f(n) - 2 \)[/tex] with an initial term [tex]\( f(1) = 18 \)[/tex], we will calculate each term step-by-step:

1. Starting with the initial term:
[tex]\[ f(1) = 18 \][/tex]

2. Calculate the second term [tex]\( f(2) \)[/tex]:
[tex]\[ f(2) = f(1) - 2 = 18 - 2 = 16 \][/tex]

3. Calculate the third term [tex]\( f(3) \)[/tex]:
[tex]\[ f(3) = f(2) - 2 = 16 - 2 = 14 \][/tex]

4. Calculate the fourth term [tex]\( f(4) \)[/tex]:
[tex]\[ f(4) = f(3) - 2 = 14 - 2 = 12 \][/tex]

5. Calculate the fifth term [tex]\( f(5) \)[/tex]:
[tex]\[ f(5) = f(4) - 2 = 12 - 2 = 10 \][/tex]

Therefore, the value of [tex]\( f(5) \)[/tex] is [tex]\( 10 \)[/tex].