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

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.

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 ) .

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.

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 .