Question

A sequence is defined recursively using the equation f(n + 1) = f(n) – 8. If f(1) = 100, what is f(6)? 52

Answer 1

Answer with Step-by-step explanation:

We are defined a sequence recursively as:

f(n + 1) = f(n) – 8

we are given f(1)=100

We have to find f(6)

f(2)=f(1)-8

f(3)=f(2)-8

    =f(1)-8-8

   = f(1)-16

f(4)=f(3)-8

    =f(1)-16-8

    =f(1)-24

f(5)=f(4)-8

    = f(1)-24-8

    =f(1)-32

f(6)=f(5)-8

    =f(1)-32-8

    =f(1)-40

    =100-40

   = 60

Hence, Value of f(6) given f(1)=100 is:

60

Answer 2

F(2) = f(1) - 8  = 100-8 = 92
f(3)  = f(1) - 2(8) = 100-16 = 84


so f(6) = f(1) - 5(8) = 60