The terms of the given series are (23 - 1), (33 - 1), (43 - 1), (53 - 1), (63 - 1), (73 - 1),.....
So, missing term = (83 - 1) = (512 - 1) = 511.

1st: 0.5
2nd: 0.5 + 0.05 = 0.55
3rd: 0.55 + 0.10 = 0.65
4th: 0.65 + 0.15 = 0.80
Therefore,
5th: 0.80 + 0.20= 1

The pattern is + 0.05, + 0.10, + 0.15,.....
So, missing term = 0.8 + 0.20 = 1.

The given sequence is a combination of two series :
I. 0, 3, 8, 15, 24, ? and II. 2, 5, 10, 17, 26
The pattern in each one of I and II is + 3, + 5, + 7, + 9, .....
So, missing term = 24 + 11 = 35.

The pattern is + 2, + 4, + 2, + 4, .....
So, missing term = 25 + 4 = 29.

The pattern is + 90 + 100, + 110,.....
So, missing term = 310 + 120 = 430.

The pattern is + 5, + 20, + 80, + 320, ...... i.e. + (5 x 12), + (5 x 22), + (5 x 42), + (5 x 82),.....
So, missing term = 427 + (5 x 162) = 427 + 1280 = 1707.

The pattern is - 1, x 10 + 1, - 1, x 10 + 1, - 1, x 10 + 1, .....
So, missing term = 10 x 10 + 1 = 101.

Each term in the series, except the first two terms, is the sum of the preceding two
terms.
So, missing term = 16 + 25 = 41.

The given series consists of squares of consecutive prime numbers
i.e. 22, 32, 52,.....,
112, 132, 172, 192.
So, missing term = 72 = 49.

Each term in the series is obtained by subtracting from the preceding term the number
formed by the first three digits of the preceding term.
So, missing term = 5242 - 524 = 4718.

Each term in the series, except the first two terms, is the product of the preceding two terms.
So, missing term = 16 x 128 = 2048.

The pattern is + 90 + 100, + 110,.....
So, missing term = 310 + 120 = 430.

The pattern is x 2 + 1, x 3 + 2, x 4 + 3,.....
So, missing term = 95 x 5 + 4 = 479.

Let the missing terms of the series be x1 and x2.
Thus, the sequence 2, 15, 4, 12, 6, 7, x1 x2 is a combination of two series :
I. 2, 4, 6, x1 and II. 15, 12, 7, x2I consists of consecutive even numbers.
So, missing term, x1 = 8.
The pattern in II is - 3, - 5,......So, missing term, x2 = 7 - 7 = 0.

The pattern is + 1008.
So, missing term - 6848 + 1008 = 7856.

The pattern is + 1, x 3, + 1, x 3, + 1, x 3, + 1,.....
So, missing term = 67 x 3 = 201.

The terms of the given series are 3 x l2, 3 x 22, 3 x 32, 3 x 42, 3 x 52, 3 x 62,.....
So, missing term = 3 x 72 = 3 x 49 = 147.

Each term at an even place in the series is the product of its two adjacent terms.
Thus, if the missing term be x, then we have : 7 x x = 56 or x = 56 ÷ 7 = 8.

The pattern is x 1, x 2, x 3, x 4,.....
So, missing term = 24 x 5 = 120.

The given sequence is a combination of two series :
I. 625, 125, 25, 5 and II. 5, 25, ?
The pattern in I is ÷ 5, while that in II is x 5. So, missing term = 25 x 5 = 125.