The recursive rule for a sequence is shown. an=an-1+7 a1=17 what is the explicit rule for this sequence?

Given the recursive formula:

an=a (n-1) + 7; a1=17

to get the explicit formula we proceed as follows:

common difference=7

a1=17

but the explicit formula for arithmetic sequence is:

an=a + (n-1) d

where:

a=fist term

n=number of terms

d=common difference

plugging the values in the formula we get:

an=17 + (n-1) 7

simplifying we get

an=17+7n-7

an=7n+10

Answer: an=7n+10