Question

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

Answer 1

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

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