Asequence is defined recursively using the equation f(n + 1) = f(n) – 8. if f(1)=100, what is f(6)?

Step-by-step explanation:

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

60 is your answer