2, 7, 19, 43, 99, 209, 431

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.