The value of [tex]f(6)[/tex] is [tex]f(6)=60[/tex]
Explanation:
The equation is [tex]f(n+1)=f(n)-8[/tex]
It is given that [tex]f(1)=100[/tex]
Now, we shall determine the value of [tex]f(6)[/tex]
Let us substitute [tex]n=1,2,3,4,5[/tex] in the equation [tex]f(n+1)=f(n)-8[/tex]
For [tex]n=1[/tex],
[tex]\begin{aligned}f(1+1) &=f(1)-8 \\f(2) &=100-8 \\&=92\end{aligned}[/tex]
Thus, when [tex]n=1[/tex] ⇒ [tex]f(2)=92[/tex]
For [tex]n=2[/tex],
[tex]\begin{aligned}f(2+1) &=f(2)-8 \\f(3) &=92-8 \\&=84\end{aligned}[/tex]
Thus, when [tex]n=2[/tex] ⇒ [tex]f(3)=84[/tex]
For [tex]n=3[/tex] ,
[tex]\begin{aligned}f(3+1) &=f(3)-8 \\f(4) &=84-8 \\&=76\end{aligned}[/tex]
Thus, when [tex]n=3[/tex] ⇒ [tex]f(4)=76[/tex]
For [tex]n=4[/tex],
[tex]\begin{aligned}f(4+1) &=f(4)-8 \\f(5) &=76-8 \\&=68\end{aligned}[/tex]
Thus, when [tex]n=4[/tex] ⇒ [tex]f(5)=68[/tex]
For [tex]n=5[/tex],
[tex]\begin{aligned}f(5+1) &=f(5)-8 \\f(6) &=68-8 \\&=60\end{aligned}[/tex]
Thus, when [tex]n=5[/tex] ⇒ [tex]f(6)=60[/tex]
Hence, the value of [tex]f(6)[/tex] is [tex]f(6)=60[/tex]
