4, 12, 36,?, 324, 972

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
+6, +9, +12, +15....
? Missing term = 6 + 6 = 12

Given series is a consecutive prime number series. Therefore, the next term will be 23.

If 10 circular plates each of thickness 3 cm, each are placed one above the other, then it forms a cylinder with height (3 x 10 = 30 cm) and a hemisphere of radius 6 cm is placed on the top just to cover the cylinder that means its radius is 6 cm also
? Radius of hemisphere (R) = 6 cm
Radius of cylinder (r) = 6 cm
and height of cylinder (h) = 30 cm
? Volume of the solid = Volume of cylinder + Volume of hemisphere
= ?r²h + (2/3)?R³
= ?(6)² x 30 + (2/3)?(6)³
= ? x 36 x 30 + (2/3)? x 216
= 1080? + 2? x 72 = 1080? + 144?
= 1224? cm³
Which is the required volume of solid.

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

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

Series pattern
(2 x Previous element) - 1
? Missing term = (2 x 65) - 1 = 130 - 1 = 129

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