A sequence is defined recursively using the equation f(n + 1) = f(n) – 8. If f(1) = 100, what is f(6)?
Answers
Answered by
51
Hey mate !!
Here's the answer !!
Given : f ( 1 ) = 100
= f ( n + 1 ) = f ( n ) - 8
Substituting n = 1, we get,
=> f ( 1 + 1 ) = f ( 1 ) - 8
=> f ( 2 ) = 100 - 8 = 92
Similarly, if n = 2, then,
=> f ( 2 + 1 ) = f ( 2 ) - 8
=> f ( 3 ) = 92 - 8 = 84
So f ( 6 ) = f ( 5 ) - 8
We know that, f ( 2 ) = f ( 1 ) - 8
=> f ( 3 ) = f ( 1 ) - 8 - 8 = f ( 1 ) - 16
If the pattern continues we get,
=> f ( n ) = f ( 1 ) - 8 ( n -1 )
=> f ( 6 ) = f ( 1 ) - 8 ( 6 - 1 )
=> f ( 6 ) = 100 - 8 ( 5 ) => 100 - 40 => 60
=> f ( 6 ) = 60
Hope my answer helped !!
Cheers !!
Here's the answer !!
Given : f ( 1 ) = 100
= f ( n + 1 ) = f ( n ) - 8
Substituting n = 1, we get,
=> f ( 1 + 1 ) = f ( 1 ) - 8
=> f ( 2 ) = 100 - 8 = 92
Similarly, if n = 2, then,
=> f ( 2 + 1 ) = f ( 2 ) - 8
=> f ( 3 ) = 92 - 8 = 84
So f ( 6 ) = f ( 5 ) - 8
We know that, f ( 2 ) = f ( 1 ) - 8
=> f ( 3 ) = f ( 1 ) - 8 - 8 = f ( 1 ) - 16
If the pattern continues we get,
=> f ( n ) = f ( 1 ) - 8 ( n -1 )
=> f ( 6 ) = f ( 1 ) - 8 ( 6 - 1 )
=> f ( 6 ) = 100 - 8 ( 5 ) => 100 - 40 => 60
=> f ( 6 ) = 60
Hope my answer helped !!
Cheers !!
Answered by
5
Answer: so I’m guessing the answer is 60
Step-by-step explanation:
Similar questions