The recursive rule for a sequence is shown.

an=an-1+6

a1=39

What is the explicit rule for this sequence?

an=33n-6

an=6n+33

an=6n-33

an=33n+6

Given that the recursive formula is:

an=an-1+6

a1=39

the second term will be:

a2=a1+6

a2=39+6=45

To evaluate the explicit formula we use the formula:

an=a+d (n-1)

where

a=first term

d=common difference

From the above a1=39 and a2=45

thus

d=45-39=6

a=39

hence the explicit formula will be:

an=39+6 (n-1)

simplifying this we obtain:

an=39+6n-6

an=39-6+6n

an=6n+33

Answer: an=6n+33