Question

The recursive rule for a sequence is shown.

an=an-1+7
a^1=17
what is the explicit rule for this sequence?

A.) an=10n-7
B.)an=7n+10
C.)an=10n+7
D.)an=7n-10

Answer 1

Given that the recursive formula is:
an=an-1+7
first term is
a1=17
the second term will be:
a2=a(2-1)+7
a2=a1+7
a2=17+7
a2=24
To evaluate for the explicit formula we use the formula:
an=a+d(n-1)
where
a=first term
d=common difference
from the calculations above:
d=24-17=7
thus the explicit formula will be:
an=17+7(n-1)
an=17+7n-7
an=7n+17-7
an=7n+10

Answer: B] an=7n+10