For an arithmetic sequence, a(n) = a(1) + d*(n-1) So for n = 14, a(14) = a(1) + 13d = 46 For n = 16, a(16) = a(1) + 15d = 58 Subtracting the first equation from the second gives: 2d = 12 Dividing by 2: d = 6 Substituting into the 1st equation: a(1) + 13*6 = 46 a(1) = -32 Therefore, a(12) = a(1) + 11d = -32 + 11(6) = 34 a(n) = -32 + 11d
