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 ,..............