1+2+7+ .. +(3n-2) =n(3n-1) 2 answer

Answer 1

k=1
1 = 1(3-1)/2
suppose true for k=n. What about k=n+1?
1+2+7+...+3n-2 + 3(n+1)-2 = n(3n-1)/2 + 3(n+1)-2
= (3n^2-n + 6n+2)/2
= (3n^2+5n+2)/2
= (n+1)(3n+2)/2
= (n+1)(3(n+1)-1)/2
True