Question

Write an explicit rule for the recursive rule. a_(1)=8,a_(n)=a_(n-1)-12

Answer 1

The explicit rule for the recursive sequence a1=8, an=an-1-12 is an=20-12n.

Step-by-step explanation:

To write an explicit rule for the given recursive definition a1=8, an=an-1-12, we need to determine an equation that directly gives the value of an for any term n without having to calculate all the previous terms.

The first term is given as 8. For each subsequent term, we subtract 12. So, the second term is 8 - 12, the third term is 8 - 12 - 12, and so on. We can notice that for term n, the number 12 is subtracted (n-1) times.

Hence, the explicit formula would be an = 8 - 12(n-1). We can further simplify this formula by distributing the -12: an = 8 - 12n + 12 or an = 20 - 12n.