Number Series Pattern Recognition

The difference pattern of the series is 3, 5, 7,.... .
Hence, the next term is <span style="font-family:" arial;="" font-size:="" small;="">26 (<span style="font-family:" arial;="" font-size:="" small;="">17 + 9).

The series has difference pattern:- 4, 6, 8, 10, 12 .........
Hence, the next term is 42 (30 + 12).

The terms of the series can be obtained by subtracting 8 and 16 alternatively from the successive terms. Hence, the required term is 27 (43 - 16).

Each term in the series is the product of the digits of the preceeding term.
Thus, 6 × 6 = 36, 3 × 6 = 18 and so on.
Therefore, next term = 1 × 8 = 8

This is an A.P series with common difference 3. Therefore, the next term is 20 (17 + 3).

The series has a difference pattern:- 1, 2, 3, 4......
So, the next term is <span style="font-family:" arial;="" font-size:="" small;="">16 (<span style="font-family:" arial;="" font-size:="" small;="">11 + 5). 

The series follows the difference pattern of 4, 8, 12, 16, 20.............
Therefore, the next term is  61 (41 + 20).

The difference pattern of the series is 1, 3, 5, 7, 9............. 
Hence, the next term will be 26 (17 + 9).

Terms are 1², 2². 3², 4², 5², 6², 7²
Hence, 5² = 25 is the missing term.

The difference pattern of the series is : 1², 2², 3², 4², 5²
Hence, next term is 56 (31 + 5^2_) . 

The series follows the following pattern:
2 x 3 + 1 = 7
7 x 3 + 3 = 24
24 x 3 + 5 = 77
77 x 3 + 7 = 238
Therefore, 238 is the next term.

The difference pattern of the series is 4, 8, 16, 32............
Therefore, next term is 63 (31 + 32).

The series follows the following pattern:
3 x 2 = 6
6 + 2 = 8
8 x 2 = 16
16 + 3 = 19
19 x 2 = 38
Thus, next term is 38.

The given series is mix of two series: 5, 10, 20, ..........and 6, 12, 24, ................
The pattern of first series:
5 x 2 = 10
10 x 2 = 20
20 x 2 = 40
and so on.
The pattern of second series:
6 x 2 = 12 
12 x 2 = 24
24 x 2 = 48
and so on.
Thus, next term is 24.

The given series is obtained by adding 1 to all the terms of the series 1³, 2³, 3³, 4³, 5³, 6³.
Hence, next term is <span style="font-family:" arial;="" font-size:="" small;="">217 (<span style="font-family:" arial;="" font-size:="" small;="">6<sup style="font-family:" arial;="">3 <span style="font-family:" arial;="" font-size:="" small;="">+ 1). 

The pattern of the series: 1² + 1, 2² + 1, 3² + 1, 4² + 1
The next term will be  26 (<span style="font-family:" arial;="" font-size:="" small;="">5<sup style="font-family:" arial;="">2 <span style="font-family:" arial;="" font-size:="" small;="">+ 1)<span style="font-family:" arial;="" font-size:="" small;="">.

The series pattern is 3 × 2 + 1 = 7, 7 × 2 + 1 = 15, 15 × 2 + 1 = 31, 31 × 2 + 1 = 63.
Thus, next term is 63.

The series is 8, 9, 15, 17, x, 9, 8. This appears to be two interleaved series: 8, 15, x, 8 and 9, 17, 9. This does not form a clear pattern. However, looking at the sequence 8, 9, 15, 17, 15, 9, 8, it is a symmetric sequence.

The terms are successively multiplied by 3, 4, 5, 6 ........so on. Therefore, the next term is 1080.

 The given series folllows the pattern:
1³ - 1 = 0
2³ - 1 = 7
3³ - 1 = 26
4³ - 1 = 63
5³ - 1 = 124
6³ - 1 = 215
Hence, next term is 215.

All the terms in the given series are prime numbers. Thus, next term is 13.

The series is mixed of two series: 2, 3, 4, 5, 6,........ and 6, 7, 8, 9,...........
Thus, the next term is 9.

The pattern of the series: 0³, 1³, 2³, 3³, 4^3, 5³.........
Hence, next term is 125.

The terms of the given series are the squares of the terms of the series 2, 5, 8, 11, 14, 17................
Therefore, next term is 289 (17²).