The given series is 1000, 1012, 988, 1024, 978

1000

1000 + 12 = 1012

1012 - 24 = 988

988 + 36 = 1024

1024 - 48 = 976 (Not 978)

The given series is 8, 14, 24, 60, 180

8

8 x 1.5 = 12 (NOT 14)

12 x 2 = 24

24 x 2.5 = 60

60 x 3 = 180

Hence, the odd man in the given series is 12.

The given number series is 3  24  186  1008  5040  20160

Here  the given series follows a pattern that,

3

3 x 8 = 24

24 x 7 = 168 not 186

168 x 6 = 1008

1008 x 5 =  5040

5040 x 4 = 20160

Hence the Odd One in the number series is 186.

Next number of the sequence 1, 4, 12, 32,...

1 = 2 x  2 0

4 = 2 x  2 1

12 = 3 x  2 2

32 = 4 x  2 3

80 = 5 x  2 4.

Here the given number series is 0, 3, 8, 15, 24, ?

The next number in the given series can be found such a way that the number series follows a pattern,

$$\begin{gathered} 2 2 - 4 = 0 \\ 3 2 - 6 = 3 \\ 4 2 - 8 = 8 \\ 5 2 - 10 = 15 \\ 6 2 - 12 = 24 \\ 7 2 - 14 = 35 \\ Hence , the next number in the iven series is 35 . \end{gathered}$$

3, 7, 6, 5, 9, 3, 12, 1, 15, ... has two different series

1) 3, 6, 9, 12, 15.....

2) 7, 5, 3, 1, .....

-1 is the next number.

The given number series is 50, 51, 47, 56, 40, ?

$$\begin{gathered} 50 \\ 50 + 1 2 = 51 \\ 51 - 2 2 = 47 \\ 47 + 3 2 = 56 \\ 56 - 4 2 = 40 \\ 40 + 5 2 = 65 \end{gathered}$$

Hence, the next number in the given number series is 65.

Given Series is 5, 14, 42, 107, 233, _?

5, 14, 42, 107, 233, _?

Differences is 9, 28, 65, 126

9 = 2^3 + 1

28 = 3^3 + 1

65 = 4^3 + 1

126 = 5^3 + 1

Now, next difference must be 6^3 + 1 = 217

Hence, next number in the given series = 233 + 217 = 450.

The given number series is 3, 5, 13, 43, 167

3

3 x 1 + 2 = 5

5 x 2 + 3 = 13

13 x 3 + 4 = 43

43 x 4 + 5 = 177 (not equal to 167)

Hence, the odd number in the given number sequence is 167.