Question

A sequence is defined by the recursive formula f (n + 1) = f(n) – 2. If f(1) = 18, what is f(5)?

Answer 1

hello :
this is the arithmetic - sequence when the common diference is : d = -2
the general term is : f(n) =f(1) +(n-1)d .. d= -2 and f(1) =18
let : n= 5
f(5) = f(1) +(5-1)(-2)
f(5) = 18 -8 = 10

Answer 2

we have
`f(n+1)=f(n)-2` with
`f(1)=18`
so

`f(2)=f(1)-2=18-2=16,\\ f(3)=f(2)-2=14,\\ f(4)=f(3)-2=12,\\ f(5)=f(4)-2=10.`
Hence
`f(5)=10.`