Question

Which sequence is generated by the function f(n + 1) = f(n) – 2 for f(1) = 10?

Answer 1

The sequence will be:  $8, 6, 4, 2, 0, -2,.......$

Explanation

Given function is:   $f(n + 1) = f(n)-2$  for  $f(1)=10$

For generating the sequence, we will just plug $n= 1,2,3,4,5,.......$ into the given function.

For $n=1$ ...  

$f(1+1)=f(1)-2\\ f(2)= 10-2=8$

For $n=2$ ...  

$f(2+1)=f(2)-2\\ f(3)= 8-2=6$

For $n=3$ ...  

$f(3+1)=f(3)-2\\ f(4)= 6-2=4$

For $n=4$ ...  

$f(4+1)=f(4)-2\\ f(5)= 4-2=2$

For $n=5$ ...  

$f(5+1)=f(5)-2\\ f(6)= 2-2=0$

For $n=6$ ...  

$f(6+1)=f(6)-2\\ f(7)= 0-2=-2$

and so on.......

So, the sequence will be:  $8, 6, 4, 2, 0, -2,.......$