Number Series
Direction: In each of the following questions, a number series is given in which one number is wrong. You have to find out that number and have to follow the new series which will be started by that number. By following this, which will be the 2nd number of the new series?
- 1 , 2 , 6 , 33 ,148 , 765 , 4626
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From above given series , we can see that
Next term = Previous term × variable + variable2
First term = 1
Second term = First term × 1 + 12 = ( 1 x 1 ) + 1 = 2
Third term = Second term × 2 + 22 = 2 x 2 + 4 = 8
Fourth term = Third term × 3 + 32 = 8 x 3 + 9 = 33
Fifth term = Fourth term × 4 + 42 = 33 x 4 + 16 = 148
Similarly , we can calculate all next terms also.
......... and so on .
Third term = Second term × 2 + 22 = 6; 6 is wrong. It should be 8. as third term .
New series is given as :-
First term = wrong term × 1 + 12 = 6 × 1 + 12 = 7;Correct Option: C
From above given series , we can see that
Next term = Previous term × variable + variable2
First term = 1
Second term = First term × 1 + 12
⇒ Second term = 1 × 1 + 12 = 1 + 1 = 2 ;
Third term = Second term × 2 + 22
⇒ Third term = 2 × 2 + 22 = 4 + 4 = 6; 6 is wrong. It should be 8. Here, 6 is the wrong number.
Similarly , we can find all others terms also.
Fourth term = Third term × 3 + 32
⇒ Fourth term = 8 × 3 + 32 = 24 + 9 = 33 ;
Fifth term = Fourth term × 4 + 42
⇒ Fifth term = 33 × 4 + 42 = 132 + 16 = 148 ;
Sixth term = Fifth term × 5 + 52
⇒ Sixth term = 148 × 5 + 52 = 740 + 25 = 765 ;
Seventh term = Sixth term × 6 + 62
⇒ Seventh term = 765 × 6 + 62 = 4590 + 36 = 4626 .
New series is given as :-
First term = wrong term × 1 + 12 = 6 × 1 + 12 = 7;
Second term = wrong term × 1 + 12 = 6 × 2 + 22 = 16.
Hence Second term of new series is 16 .
