Pattern Recognition - 117

If      1  = 2
        2  = 10
        3  = 30
        4  = 68
        5  =  ?

(Taken from internet)

Answer

Tn = (n*n *n) +n
T1 = (1*1 *1) +1 = 2
T2 = (2* 2 *2) +2 =10
T3 = (3* 3* 3) +3 =30
T4 = (4* 4 *4) +4 =68
T5 = (5* 5* 5) +5 =130

5= 130

Pattern Recognition - 116

Find out the next two numbers in the series.
253 , 351 , 152 , 250 , 51,_ , _ ,.................

Answer

Tn-1 = Reverse form(Tn)  - 1
351 = Reverse(253) -1
152 = Reverse(351) -1
250 = Reverse(152) -1
51  = Reverse(250) -1

Next two numbers  
Reverse(51) -1 =14 
Reverse(14) -1 =40

253 , 351 , 152 , 250 , 51, 14 , 40,.................

Pattern Recognition - 115

Find out the next two numbers in the series.
6 , 48 , 342 , 2400 , _ , _ , ...................................

Answer

Tn = (7 ^ n) -1  
T1=7^1  -1  =6 
T2=7^2  -1  =48 
T3=7^3  -1  =342
T4=7^4  -1  =2400
T5=7^5  -1  =16806 
T6=7^6  -1  =117648

6 , 48 , 342 , 2400 , 16806 , 117648 , ...................................

Pattern Recognition - 114

Find out the next two numbers in the series.
5 ,6 , 4 , 7 , 3 , 8 ,2 ,_ ,_ ,..............


Answer

5 ,   6 ,   4 ,    7 ,     3 ,     8 ,     2 ,_ ,_ ,..............
   +1   -2    +3    -4      +5    -6

Next two numbers  2 + 7 = 9  
                           9  - 8 = 1

5 ,   6 ,   4 ,    7 ,     3 ,     8 ,     2 ,  9 , 1 ,..............

Pattern Recognition - 113

If
5 +2 =17
4+3 =19
7+2 =23

then 6+1 =?


Answer

5 + 2  => (5*2) +5 +2 =17
4 + 3  => (4*3) +4 + 3 =19
7 + 2  => (7* 2) + 7 +2=23

6+ 1   => (6*1)+6 +1 = 13

Pattern Recognition - 112

Find out the next two numbers in the series.
120813 , 141015 , 161219 , 181427 , _ , _ ,..................


Answer

120813 , 141015 , 161219 , 181427 , _ , _ ,..................
120813 , 141015 , 161219 , 181427 , _ , _ ,..................
120813 , 141015 , 161219 , 181427 , _ , _ ,..................

12 ,  14 ,   16 ,   18 ,_ ,_,............................... Next two numbers 20 , 22
     +2    +2     +2
08 ,  10 ,  12    , 14,_,_ ,.............................   Next two numbers 16, 18
    +2     +2    +2
13, 15 ,   19 ,   27 , _ , _ ,..................Next two numbers 27+16=43,43+32=75
   +2  +4     +8

Next two numbers in the original series  201643 , 221875
120813 , 141015 , 161219 , 181427 , 201643 , 221875 ,..................

Pattern Recognition - 111

Find out the next two numbers in the series.
6616 , 5814 , 5012 , 4210, _ , _ , .....................


Answer

6616 , 5814 , 5012 , 4210, _ , _ , ..................... 
66 , 58 , 50 ,42 ,.........   Next two numbers 34,26
6616 , 5814 , 5012 , 4210, _ , _ , .....................
16 , 14 , 12 , 10 ,........... Next two numbers  8,6

Next two numbers in the original series 348 , 266
6616 , 5814 , 5012 , 4210, 348 , 266 , .....................

There was another answer from some one at office - 3408, 2606 . I think that is also a correct answer. (to keep the number of digits(4) consistent)