Question

A sequence is defined recursively using the equation f(n + 1) = f(n) – 8. If f(1) = 100, what is f(6)? 608

Answer 1

Since, A sequence is defined recursively using the equation f(n + 1) = f(n) – 8.

If f(1) = 100,we have to find the value of f(6).

Consider

$f(n+1) = f(n)-8$

Let n =1, we get

$f(1+1) =f(2)= f(1)-8= 100-8 = 92$

Let n =2, we get

$f(2+1) =f(3)= f(2)-8= 92-8 = 84$

Let n =3, we get

$f(3+1) =f(4)= f(3)-8= 84-8 = 76$

Let n =4, we get

$f(4+1) =f(5)= f(4)-8= 76-8 = 68$

Let n =5, we get

$f(5+1) =f(6)= f(5)-8= 68-8 = 60$

Therefore, the value of f(6) is 60.