The first difference is +5 +7 +9 +11 The second difference is +2 Half the second difference to get the coefficient of n^2 So it will be n^2 Compare n^2 to original sequence 1 4 9 16 25 36 3 8 15 24 35 The difference between the two is +2 +4 +6 +3 This is a linear sequence with the nth term of 2n so the nth term is n^2 +2n
