Question

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

Answer 1

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