Pattern Recognition - 153

Find out the next two numbers in the series.
124576 ,24576, 8101412, 80832816,_,_,.................

Answer

124576 ,24576, 8101412, 80832816,_,_,.................

24576      =(1*2)(1*4)(1*5)(1*7)(1*6)

8101412  =(2*4)(2*5)(2*7)(2*6) 

80832816=(8*1)(8*0)(8*1)(8*6) (8*4)(8*6) (8*1)(8*2) 

Next two numbers

(8*0)(8*8)(8*3)(8*2) (8*8)(8*1) (8*6) =064241664848 = 64241664848

(6*4)(6*2)(6*4)(6*1) (6*6)(6*6) (6*4)(6*8)(6*4) (6*8) =24  12 24 6 36 36 24 48 24 48

124576 ,24576, 8101412, 80832816,   64241664848, 2412246363624482448 ,.................

Pattern Recognition - 152

Find out the next two numbers in the series.
86371 , 74855, 63541, _ ,_ ,.........................

Answer

86371 ,  74855,  63541, _ ,_ ,.........................

86371

63=(8 *8) -1

71=(8*9) -1

74855

48=(7 *7) -1

55=(7*8) -1

63541

35=(6 *6) -1

41=(6*7) -1

Next two numbers  

 5  (5*5)-1   (5*6)-1 = 52429

4  (4*4)-1   (4*5)-1 =  41519

86371 , 74855, 63541,52429 ,41519 ,.........................

Pattern Recognition - 151

Find out the next two numbers in the series.
185 , 326 , 507 , 728 , _ , _ ,.....................

Answer

185 , 326 , 507 , 728 , _ , _ ,.....................

185 , 326 , 507 , 728 , _ , _ ,

                185 ,                            326                ,    507 ,                     728 , _ , _ ,

(5-2)^2 *2 =18     (6-2)^2 *2 =32     (7-2)^2 *2 =50    (8-2)^2 *2 =72

Next two numbers   (9-2)^2 *2   =98      989

                              (10-2)^2 *2 =128     12810

185 , 326 , 507 , 728 , 989 , 12810,.....................

However there was a brilliant answer for the given wrong question from some one in our team. :)     

185 , 326 , 987 , 728 , 189, 320

xyz, lastdigit of(x*3), 8 and 2 repeating, (z+1)

How I saw is to get the first digit,
multiply the number by 3
1, 3, 9, 27, 81 ...
and then take the last digit only,
so it goes as 1,3,9,7,1....

Pattern Recognition - 150

Find out the next two numbers in the series.
14 , 27 , 80 , 319 ,1594 , _ , _ ,..............

Answer

14 , 27 , 80 , 319 ,1594 , _ , _ ,..............

Tn= (Tn-1 * n )- 1

T2= (T1 * 2 )- 1 =(14*2) -1 =27

T3= (T2 * 3 ) -1 =(27*3) -1 =80

T4= (T3 * 4 ) -1 =(80*4) -1 =319

T5= (T4* 5 ) -1 =(319*5) -1=1594

Next two numbers 

T6 = (T5* 6)-1 = (1594*6) -1=9563

T7=  (T6*7)-1  = (9563*7) -1=66940

14 , 27 , 80 , 319 ,1594 , 9563 , 66940 ,..............