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

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