Question

Which sequence is generated by the function f(n + 1) = f(n) – 2 for f(1) = 10? –10, –12, –14, –16, –18, ... –2, 8, 18, 28, 38, ... 8, 18, 28, 38, 48, ... 10, 8, 6, 4, 2, ...

Answer 1

The correct option will be:   10, 8, 6, 4, 2, ...

Explanation

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

For finding the sequence, we will plug $n= 1,2,3,4,......$ into the given function one by one. So......

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 $n=4$.....

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

Now, the sequence will be in form of:   $f(1), f(2), f(3), f(4), f(5),........$

So, the sequence will be:  10, 8, 6, 4, 2, ..........