Question

A sequence is defined recursively using the equation f(n + 1) = f(n) – 8. If f(1) = 100, what is f(6)

Answer 1

\[f(n+1)=f(n)-8 , put,n= 1\implies f(1+1)=f(2)=f(1)-8=100-8=92\] repeat this process for n=2,3,4,5
\[f(2+1)=f(3)=f(2)-1=92-8=84\]
\[f(3+1)=f(4)=f(3)-1=84-8=76\]
\[f(4+1)=f(5)=f(4)-8=76-8=68\]
\[f(5+1)=f(6)=f(5)-8=68-8=60\]
\[\therefore f(6)=60\]