2, 7, 28, 146, 877, 6140

As per the details in the question the series is in the form of
First term = 2
Second term = ( First term × 3 ) + 1
? Second term = ( 2 × 3 ) + 1 = 7
Third term = ( Second term × 4 ) + 1
? Third term = ( 7 × 4 ) + 1 = 28 is wrong , 29 should be sixth term because ( 7 × 4 ) + 1 = 29 .
So 28 is wrong. we get 29 as Third term.
Fourth term = ( Third term × 5 ) + 1
? Fourth term = ( 29 × 5 ) + 1 = 146
Fifth term = ( Fourth term × 6 ) + 1
? Fifth term = ( 146 × 6 ) + 1 = 877