I don't get these questions I just need help understanding them to understand my work better

Show your work for full credit. 1- The arithmetic sequence { -2, 1, 4, 7,... } is given. a) Write a recursive formula. b) Write an explicit formula for the nth term. c) Find the sum of first 30 terms. 2- The geometric sequence { 3, 6, 12, 24,.. } is given. a) Write a recursive formula. b) Write an explicit formula for the nth term. c) Find the sum of first 10 terms. 3- Using mathematical induction, prove that 1 + 2 + 3 + .. + n =- n(n+1) 2