What is the recursive rule for the following sequence: - 9, - 2, 5, 12, ...

A) an = a n-1 - 9

B) an = a n-1 + 9

C) an = a n-1 + 7

D) an = a n-1 - 7

The answer is option (C) = an-1+7

Step-by-step explanation:

A recursive rule is a formula that in which each term is expressed as a function of its preceding term (s), meaning in order to get to the nth term you have to express it in a form of the term that comes before it. In our case the a (n-1) term

So for the sequence - 9, - 2, 5, 12

The nth term is any number on the sequence and

-2 is the a (n-1) term for - 9 5 is the a (n-1) term for - 2 12 is the a (n-1) term for 5

So we need to find out what we have to do to the preceding term to get the next.

To get - 2 from - 9 we have to add 7 to - 9; - 9+7=-2

To get 5 from - 2 we have to add 7 to - 2; - 2+7=5

To get 12 from 5 we add 7 to 5; 7+5=12

So the recursive rule would be = a n-1+7