Question

A sequence is defined by the formula f(n+1)=f(n)-3. If f(4)=22, what is f(1)?

Answer 1

The value of f(1) is 31

Solution:

Given that the sequence is defined by formula:

$f(n+1) = f(n) - 3$

To find: f( 1 )

Also given that,

$f(4) = 22$

So, we can say,

$f(4) = f(3+1) = 22$

Substitute n = 3 in given formula

$f(3+1) = f(3) - 3\\\\f(4) = f(3) - 3\\\\Substitute\ f(4) = 22\\\\22 = f(3) -3\\\\f(3) = 25$

Now we got, f(3) = 25

Use the similar steps to find for f(2)

Substitute n = 2 in given function

$f(2+1) = f(2) - 3 \\\\f(3) = f(2) -3\\\\25 = f(2) - 3\\\\f(2) = 28$

Use the similar steps to find for f(1)

Substitute n = 1 in given function

$f(1+1) = f(1) - 3\\\\f(2) = f(1) - 3\\\\28 = f(1) - 3\\\\f(1) = 28+3\\\\f(1) = 31$

Thus value of f(1) is 31