Go on dividing by 6, 5, 4, 3, 2, 1 respectively to obtain the next number. Clearly, 92 is wrong.

Go on multiplying the number by 2 and adding 1 to it to get the next number. So, 27 is wrong.

Let the given number be A, B, C, D, E, F, G. Then A x 1 + 1, B x 2 + 2, C x 3 + 3, D x 4 + 4, E x 5 + 5, F x 6 + 6 are the required number . Clearly, 228 is wrong.

Go on subtracting prime numbers 19, 17, 13, 11, 7, 5 from the number to get the next number. So, 88 is wrong.

The pattern is
1² ,
1² + 2²,
1² + 2² + 3²,
1² + 2² + 3² + 4²,
1² + 2² + 3² + 4² + 5²,
1² + 2² + 3² + 4² + 5² + 6² .
But 50 is not of this pattern.

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

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

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

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

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