Number Series
Direction: In each of these questions a number series is given. Only one number is wrong in each series. You have to find out the wrong number.
 1, 3, 9, 31, 128, 651, 3913

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As per the details in the question the series is in the form of
Next term = ( Previous term × variable ) + ( 1 + variable )
First term = 1
Second term = First term × 1 + 2 = 3
Third term = Second term × 2 + 3 = 9
Similarly , we can calculate all next terms also.Correct Option: B
As per the details in the question the series is in the form of
Next term = ( Previous term × variable ) + ( 1 + variable )
First term = 1
Second term = First term × 1 + 2
⇒ Second term = 1 × 1 + 2 = 3 ;
Third term = Second term × 2 + 3
⇒ Third term = 3 × 2 + 3 = 9 ;
Similarly , we can find all others terms also.
Fourth term = Third term × 3 + 4
⇒ Fourth term = 9 × 3 + 4 = 31 ;
Fifth term = Fourth term × 4 + 5
⇒ Fifth term = 31 × 4 + 5 = 128 , is wrong . it should be 129 as fifth term .
Sixth term = Fifth term × 5 + 6
⇒ Sixth term = 129 × 5 + 6 = 651 ;
Seventh term = Sixth term × 6 + 7
⇒ Seventh term = 651 × 6 + 7 = 3913
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?
 11 , 18 , 39 , 97.5 , 295.5 ,1037.75

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As per the details in the question the series is in the form of
Next term = Previous term × variable +variable
First term = 11
Second term = First term × 1.5 + 1.5 = 18
Third term = Second term × 2 + 2 = 39 , is wrong . it should be 38 as third term .
Similarly , we can calculate all next terms also.
New series is given as 
First term = 39 × 1.5 + 1.5 = 60;
Second term = 60 × 2 + 2 = 122.
Hence Second term of new series is 122.Correct Option: A
As per the details in the question the series is in the form of
Next term = Previous term × variable +variable
First term = 11
Second term = First term × 1.5 + 1.5
⇒ Second term = 11 × 1.5 + 1.5 = 18 ;
Third term = Second term × 2 + 2
⇒ Third term = 18 × 2 + 2 = 39 , is wrong . it should be 38 as third term .
Similarly , we can find all others terms also.
Fourth term = Third term × 2.5 + 2.5
⇒ Fourth term = 38 × 2.5 + 2.5 = 97.5 ;
Fifth term = Fourth term × 3 + 3
⇒ Fifth term = 97.5 × 3 + 3 = 295.5 ;
Sixth term = Fifth term × 3.5 + 3.5
⇒ Sixth term = 295.5 × 3.5 + 3.5 = 1037.75 ;
New series is given as 
First term = 39 × 1.5 + 1.5 = 60;
Second term = 60 × 2 + 2 = 122.
Hence Second term of new series is 122.
 2 , 9 , 5 , 36 , 125 , 648 , 3861

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As per the details in the question the series is in the form of
First term = 2
Second term = First term × 1 + 7 = 9
Third term = Second term × 2  11 = 5
Similarly , we can calculate all next terms also.Correct Option: E
As per the details in the question the series is in the form of
First term = 2
Second term = First term × 1 + 7
⇒ Second term = 2 × 1 + 7 = 2 + 7 = 9 ;
Third term = Second term × 2  11
⇒ Third term = 9 × 2  11 = 18  11 = 5; 5 is wrong. It should be 7 as Third term .
Similarly , we can find all others terms also.
Fourth term = Third term × 3 + 15
⇒ Fourth term = 7 × 3 + 15 = 21 + 15 = 36 ;
Fifth term = Fourth term × 4  19
⇒ Fifth term = 36 × 4  19 = 144 19 = 125 ;
Sixth term = Fifth term × 5 + 23
⇒ Sixth term = 125 × 5 + 23 = 625 + 23 = 648 ;
Seventh term = Sixth term × 6  27
⇒ Seventh term = 648 × 6  27 = 3888  27 = 3861 .
New series is
First term = 5 × 1 + 7 = 12;
Second term = 12 × 2  11 = 13.
Hence Second term of new series is 13 and correct option is ( E ) .
 2, 7, 19, 43, 99, 209, 431

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The given series is in the below pattern,
First term = 2
Second term = ( First term × 2 ) + 3 = 7 ;
Third term = ( Second term × 2 ) + 5 = 19 ;
Similarly , we can calculate all others terms also.
.......... and so on .
New series is given as 
First term = 43 × 2 + 3 = 89;
Second term = 89 × 2 + 5 = 181.
Hence Second term of new series is 181.Correct Option: C
The given series is in the below pattern,
First term = 2
Second term = ( First term × 2 ) + 3
⇒ Second term = ( 2 × 2 ) + 3 = 7 ;
Third term = ( Second term × 2 ) + 5
⇒ Third term = ( 7 × 2 ) + 5 = 19
Similarly , we can calculate all others terms also.
Fourth term = ( Third term × 2 ) + 7
⇒ Fourth term = ( 19 × 2 ) + 7 = 43 , is wrong.it should be 45 as fourth term .
Fifth term = ( Fourth term × 2 ) + 9
⇒ Fifth term = ( 45 × 2 ) + 9 = 99 ;
Sixth term = ( Fifth term × 2 ) + 11
⇒ Sixth term = ( 99 × 2 ) + 11 = 209 ;
Seventh term = ( Sixth term × 2 ) + 11
⇒ Seventh term = ( 209 × 2 ) + 13 = 431
New series is given as 
First term = 43 × 2 + 3 = 89;
Second term = 89 × 2 + 5 = 181.
Hence Second term of new series is 181.
 1 , 2 , 6 , 33 ,148 , 765 , 4626

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From above given series , we can see that
Next term = Previous term × variable + variable^{2}
First term = 1
Second term = First term × 1 + 1^{2} = ( 1 x 1 ) + 1 = 2
Third term = Second term × 2 + 2^{2} = 2 x 2 + 4 = 8
Fourth term = Third term × 3 + 3^{2} = 8 x 3 + 9 = 33
Fifth term = Fourth term × 4 + 4^{2} = 33 x 4 + 16 = 148
Similarly , we can calculate all next terms also.
......... and so on .
Third term = Second term × 2 + 2^{2} = 6; 6 is wrong. It should be 8. as third term .
New series is given as :
First term = wrong term × 1 + 1^{2} = 6 × 1 + 1^{2} = 7;Correct Option: C
From above given series , we can see that
Next term = Previous term × variable + variable^{2}
First term = 1
Second term = First term × 1 + 1^{2}
⇒ Second term = 1 × 1 + 1^{2} = 1 + 1 = 2 ;
Third term = Second term × 2 + 2^{2}
⇒ Third term = 2 × 2 + 2^{2} = 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 + 3^{2}
⇒ Fourth term = 8 × 3 + 3^{2} = 24 + 9 = 33 ;
Fifth term = Fourth term × 4 + 4^{2}
⇒ Fifth term = 33 × 4 + 4^{2} = 132 + 16 = 148 ;
Sixth term = Fifth term × 5 + 5^{2}
⇒ Sixth term = 148 × 5 + 5^{2} = 740 + 25 = 765 ;
Seventh term = Sixth term × 6 + 6^{2}
⇒ Seventh term = 765 × 6 + 6^{2} = 4590 + 36 = 4626 .
New series is given as :
First term = wrong term × 1 + 1^{2} = 6 × 1 + 1^{2} = 7;
Second term = wrong term × 1 + 1^{2} = 6 × 2 + 2^{2} = 16.
Hence Second term of new series is 16 .