Pattern Recognition - 24

Find the next two numbers in the series.

1,3,15,105,945,_,_,.......



Answer

3      =  1    *  3
15    =  3    *  5
105  =  15  *  7
945  =  105*  9

Next two numbers

945    *   11=  10395
10395 *  13 = 135135


1 ,3 ,15 ,105 ,945, 10395 , 135135,......

Pattern Recognition - 23

Find the next two numbers in the series.

1,2,5,26,677,_,_,....... 


Answer

Tn=(Tn-1) ^ 2 +1                       

n^2 means n*n


2     =(1 * 1)+1
5     =(2*2)+1
26   =(5*5)+1
677 =(26*26)+1


Next two numbers


(677*677)+1=458330
(458329 * 458329)+1=210066388901


1, 2 , 5 ,26 ,677 , 458330, 210066388901,.......

Pattern Recognition- 22

Find the next two numbers in the series.

2011 ,2013 , 2017 ,2019 ,2023 ,_,_,.........

Answer

2011 ,2013 , 2017 ,2019 ,2023 ,_,_,.........

11,13,17,19,23,_,_

We could consider the above series as prime number series starting from 11.
Next two numbers will be 29,31


2011 ,2013 , 2017 ,2019 ,2023 ,2029,2031,.........


It can be taken in this way too.

11,    13,   17,   19,  23, _  ,  _
    +2    +4   +2   +4

Next two numbers  23+2=25
                              25+4=29


2011 ,2013 , 2017 ,2019 ,2023 ,2025,2029,.........

Pattern Recognition-21

Find the next two numbers in the series.

20 ,35 ,47 ,59 ,611 ,713 ,_,_,.......


Answer

20 -----  2         0
35 -----  3         5        2+1     (2*2 )+ 1
47 ------ 4         7        3+1     (3*2)+ 1
59 ------ 5         9        4+1     (4*2)+ 1
611----- 6        11       5+1     (5*2)+ 1
713------7       13       6+1     (6*2)+ 1

Next two numbers

7+1     (7*2)+1           8  15   =815
8+1     (8*2)+1           9  17   =917


20 ,35 ,47 ,59 ,611 ,713,815,917,.......

Pattern Recognition -20

Find the next two numbers in the series.

8179 , 7186 , 6157 ,5164 ,4135 , _, _


Answer

8179 , 7186 , 6157 ,5164 ,4135 , _, _

8179 ----> 7=8-1       9=8+1     - , +

7186----->8=7+1      6=7-1       +, -

6157-------->5=6-1            7= 6+1              -, +

5164 ------> 6= 5 + 1         4=5-1               +, -

4135 --->3=4-1        5=4+1       -, +


Next two numbers

31 ------>   +, -   3+1 =4     3-1=2          3142
21------->    -, +  2-1=1       2+1=3         2113

8179 , 7186 , 6157 ,5164 ,4135 , 3142, 2113,........

Pattern Recognition -19

Find the next two numbers in the series.

8, 5 , 3 ,13 , 10 , 8 , 25 , 22 , 20 , 32 , _ , _

Answer

8 ,   5,      3,     13 ,    10,    8     25 ,   22  ,   20  
  -3      -2               -3       -2           -3     -2


Next two numbers

32
32-3=29
29-2=27



8, 5 , 3 ,13 , 10 , 8 , 25 , 22 , 20 , 32 , 29 , 27,........

Pattern Recognition - 18

Find the next two numbers in the series.

13 ,62 ,421 ,248 ,694 ,_ ,_,......


Answer

Tn=Reverse (Tn-1 * 2)

62 = Reverse (13*2)
421=Reverse (62*2)
248=Reverse (421*2)
694=Reverse (248*2)

Next two numbers will be

Reverse (694*2) => 1388 => 8831
Reverse (8831 *2)=>17662 =>26671

13 ,62 ,421 ,248 ,694 ,8831 ,26671, _, _ ,......

 
 
When I shared the same question on my office blog, some body came up with this answer. It is also a correct answer.

62x4=248x4=992x4=3968

I don't know the 'official' way to indicate reversing numbers, so just follow the number to be reversed with an R:

13R=31x2=62;
421R=124x2=248;
694R=496x2=992;
4891R=1984x2=3968

13 ,62 ,421 ,248 ,694 ,992,3968, _, _ ,......