Question

Write a rule for the nth term of the sequence 2,20,50,92?

Answer 1

`2,20,50,92,...\\ \\ a_1 = 2\\ a_2 = a_1+18=a_1+6\cdot 3 \\ a_3 = a_2+30=a_2+6\cdot 5\\ a_4 = a_3 +42 = a_3+6\cdot 7\\ a_5 =a_4+54 = a_4+6\cdot 9\\...\\a_n = a_(n-1)+6\cdot (2n-1) \\ \\ a_1+a_2+...+a_n = \\ =a_1+a_2+...+a_(n-1)+2+6\cdot \Big(3+5+7+...+(2n-1)\Big)\\ \\ a_n = 2+6\cdot \Big(3+5+7+...+(2n-1)\Big)\\ a_n = 6\cdot \Big(1+3+5+7+...+(2n-1)\Big)-4 \\ a_n = 6\cdot n^2-4 \\ \\ \Rightarrow \boxed{a_n = 6n^2-4}`

Answer 2

482

Explanation:

Their 2nd difference is 12