3, 5, 9, 17, 33, 65,?

Series pattern
+3, +6, +9, +12, +15, +18
? Missing term = 57 + 18 = 75

Series pattern
1², 3², 5², 7², 9², 11²
? Missing term = 1² = 1

Series pattern
Every next element = 3 x previous element
? Missing term = 3 x 36 = 108

A = (a + b)/2,
1/H = (1/a + 1/b)/2
? H = 2ab/(a +b),
G = ?ab
? A x H = {(a + b)/2} x {2ab/(a + b)} = ab = G²
? A x H = G²

(1 - 2) = -1
(3 - 4) = -1
(5 - 6) = -1
and so on.
? Total terms of -1 will be 50.
? Answer = -1 x 50 = -50

Series pattern = (Previous element/2) - 1
Missing term = 23/2 - 1 = 10.5

Series pattern = (5 x Previous element) + 5
? Missing term = (5 x 130) + 5 = 655

Series pattern
1², 3², 5², 7², 9², 11²
So missing term = 11² = 121

Series pattern
+ 13, + 26, + 39, + 52, + 65
? Missing term = 132 + 65 = 197

Series pattern
Previous number/5
? Missing term = 244/5 = 48.8