Question

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

Answer 1

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