The recursive rule for a sequence is shown.

an=an−1+6

a1=39

What is the explicit rule for this sequence?

a_{n} = a_{n-1} + 6, a1 = 39

Note that the terms are

39, 45, 51, 55.......

So....we can write

6(1) + 33, 6(2) + 33, 6(3) + 33 , 6(4) + 33

So...the explicit rule is

a_{n} = 6_{n} + 33