The value of f(1) is 31
Solution:
Given that the sequence is defined by formula:
[tex]f(n+1) = f(n) - 3[/tex]
To find: f( 1 )
Also given that,
[tex]f(4) = 22[/tex]
So, we can say,
[tex]f(4) = f(3+1) = 22[/tex]
Substitute n = 3 in given formula
[tex]f(3+1) = f(3) - 3\\\\f(4) = f(3) - 3\\\\Substitute\ f(4) = 22\\\\22 = f(3) -3\\\\f(3) = 25[/tex]
Now we got, f(3) = 25
Use the similar steps to find for f(2)
Substitute n = 2 in given function
[tex]f(2+1) = f(2) - 3 \\\\f(3) = f(2) -3\\\\25 = f(2) - 3\\\\f(2) = 28[/tex]
Use the similar steps to find for f(1)
Substitute n = 1 in given function
[tex]f(1+1) = f(1) - 3\\\\f(2) = f(1) - 3\\\\28 = f(1) - 3\\\\f(1) = 28+3\\\\f(1) = 31[/tex]
Thus value of f(1) is 31
