Question 430428
(a)  {{{a[4] = a[1] + 3d = 16}}}, and {{{a[8] = a[1] + 7d = 4a[1]}}}
<==> {{{3a[1] = 7d}}}
==> {{{a[1] = (7d)/3}}}
==> {{{(7d)/3 + 3d = 16}}}
==> {{{(16d)/3 = 16}}}
==> d = 3
==> {{{a[1] = (7*3)/3 = 7}}}
==> T(n) = 7 + (n-1)3 = 7 + 3n - 3 = 3n + 4


(b) We want 3n + 4 > 500, or n > 165.333.....  Hence when n = 166, we get the smallest term greater than 500, which is 3*166 + 4 = 502.