The recursive rule for a sequence is shown. an=an−1+7 a1=17 what is the explicit rule for this sequence?
Accepted Solution
A:
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