The third and thirtieth term of an arithmetic sequence are 4 and 85 write an explicit rule for this sequence

An=a1+d (n-1)

a3=4=a1+d (3-1) = a1+2d

a30=85=a1+d (30-1) = a1+29d

4=a1+2d

85=a1+29d

85-4 = (a1+29d) - (a1+2d) =

81=a1-a1+29d-2d=27d

81=27d

divide both sides by 27

3=d

4=a1+3 (2)

4=a1+6

minus 6

-2=a1

an=-2+3 (n-1)

an=-2+3n-3

an=-5+3n