What is the recursive rule for an=2n+11? a1=11; an=an−1+2 a1=13; an=an−1+2 a1=13; an=an−1+11 a1=2; an=an−1+11

If we think easily
first, an = 2n+11 (1)
if n =1 so a1 = 2(1)+11 = 13 (2)
so either choice b or c is the correct answer

then we will consider about an from the formula that

an=a1+ ( n-1 )d

from (1)
2n+11 = a1 + (n-1)d
from (2)
2n+11 = 13 + (n-1)d
2n-2 = (n-1)d
so d = 2n-2 / n-1 = 2(n-1) / (n-1)
so that d=2 (3)

from (1) we will know that
a2= 2(2)+11 = 15

and from formula
we will know that
a2=a1+ d
or
an=an-1 + 2 (if n=2)

so the answer of this question is b. a1=13;an=an−1+2 #