Question

which sequance is generated by the function f(n+1)=f(n)-2 for f(1)=10

Answer 1

The given function is

$f(n+1)=f(n)-2$

We know that

$f(1)=10$

So, let's form the sequence using the function.

For n = 1.

$\begin{gathered} f(1+1)=f(1)-2 \\ f(2)=1-2 \\ f(2)=-1 \end{gathered}$

For n = 2.

$\begin{gathered} f(2+1)=f(2)-2 \\ f(3)=-1-2 \\ f(3)=-3 \end{gathered}$

For n = 3.

$\begin{gathered} f(3+1)=f(3)-2 \\ f(4)=-3-2 \\ f(4)=-5 \end{gathered}$

For n = 4.

$\begin{gathered} f(4+1)=f(4)-2 \\ f(5)=-5-2 \\ f(5)=-7 \end{gathered}$

Until now, the sequence is

$-1,-3,-5,-7,\ldots$

As you can observe, the function generates an arithmetic sequence with a difference of -2.