Question

Rewrite f(n) =2(n-1)+2 as a recursive rule

Answer 1

The recursive formula of any sequence gives us two piece of information

1. The first term

2. The pattern or rule that lets you find the given term using the term that comes before it

Here we have

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

The arithmetic sequence is given by

a+d(n-1)

a is the first term

d is called the common difference or the number that is added to the previous number every time

Here we have a=2, and d=2

Hence the recursive rule is given by

$\left \{ {{a(1)=2} \atop {a(n) = a(n-1)+2}} \right.$

This is the recursive rule for the given function

Answer 2

F(n)= 2n-3 . hope i helped