The given series is in the below pattern ,
First series :-
First term = 4
Second term = First term × 2 + 1
? Second term = 4 × 2 + 1 = 9
Third term = Second term × 3 - 2
? Third term = 9 × 3 - 2 = 25
similarly , we can find the all others terms .
......... and so on .
Second series :-
First term = 3
Second term = First term × 2 + 1
? Second term = 3 × 2 + 1 = 7
Third term = Second term × 3 - 2
? Third term = 7 × 3 - 2 = 19
Fourth term = Third term × 4 + 3
? Fourth term = 19 × 4 + 3 = 79
Hence , the place value of ( c ) is 79 .

The given series is in the below pattern ,
First series :-
First term = 6
Second term = First term × 2 - 2
? Second term = 6 × 2 - 2 = 10
Third term = Second term × 3 + 2
? Third term = 10 × 3 + 2 = 32
similarly , we can find the all others terms .
......... and so on .
Second series :-
First term = 2
Second term = First term × 2 - 2
? Second term = 2 × 2 - 2 = 2
Hence , the place value of ( a ) is 2 .

As per the details in the question the series is in the form of
First series :-
First term = 7
Second term = First term × 0.5 + 0.5
? Second term = 7 × 0.5 + 0.5 = 4
Third term = Second term × 1 + 1
? Third term = 4 × 1 + 1 = 5
similarly , we can find the all others terms .
Second series :-
First term = 3
Second term = First term × 0.5 + 0.5
? Second term = 3 × 0.5 + 0.5 = 2
Third term = Second term × 1 + 1
? Third term = 2 × 1 + 1 = 3
Fourth term = Third term × 1.5 + 1.5
? Fourth term = 3 × 1.5 + 1.5 = 6
Hence , the place value of ( c ) is 6 .

As per the details in the question the series is in the form of
First series :-
First term = 3
Second term = First term × 2 + 6
? Second term = 3 × 2 + 6 = 12
Third term = Second term × 2 + 6
? Third term = 12 × 2 + 6 = 30
similarly , we can find the all others terms .
Second series :-
First term = 7
Second term = First term × 2 + 6
? Second term = 7 × 2 + 6 = 20
Third term = Second term × 2 + 6
? Third term = 20 × 2 + 6 = 46
Hence , the place value of ( b ) is 46 .

The series is × 2 ?1, × 3 ? 2, × 4 ? 3,.....
The given series is in the below pattern ,
First series :-
First term = 2
Second term = First term × 2 - 1
? Second term = 2 × 2 - 1 = 3
Third term = Second term × 3 - 2
? Third term = 3 × 3 - 2 = 7
similarly , we can calculate the all next terms .
Second series :-
First term = 3
Second term = First term × 2 - 1
? Second term = 3 × 2 - 1 = 5
Third term = Second term × 3 - 2
? Third term = 5 × 3 - 2 = 13
Fourth term = Third term × 4 - 3
? Fourth term = 13 × 4 - 3 = 49
Hence , the place value of ( c ) is 49 .

As per the details in the question the series is in the form of
First series :-
First term = 1
Second term = First term × 1 + 7
? Second term = 1 × 1 + 7 = 8
Third term = Second term × 2 - 6
? Third term = 8 × 2 - 6 = 10
similarly , we can find the all others terms .
Second series :-
First term = 2
Second term = First term × 1 + 7
? Second term = 2 × 1 + 7 = 9
Third term = Second term × 2 - 6
? Third term = 9 × 2 - 6 = 12
Fourth term = Third term × 3 + 5
? Fourth term = 12 × 3 + 5 = 41
Hence , the place value of ( c ) is 41 .

As per the details in the question the series is in the form of
First series :-
First term = 9
Second term = First term × 2 + 1.5 = 19.5
Third term = Second term × 2 + 2 = 41
similarly , we can calculate the all next terms .
Second series :-
First term = 12
Second term = First term × 2 + 1.5 = 25.5
Third term = Second term × 2 + 2 = 53
Fourth term = Third term × 2 + 2.5
? Fourth term = 53 × 2 + 2.5 = 108.5
So, 108.5 should come in place of (c).

The given series is in the below pattern ,
First series :-
First term = 38
Second term = First term × 0.5
? Second term = 38 × 0.5 = 19
Third term = Second term × 1.5
? Third term = 19 × 1.5 = 28.5
similarly , we can find the all others terms .
Second series :-
First term = 18
Second term = First term × 0.5
? Second term = 18 × 0.5 = 9
Third term = Second term × 1.5
? Third term = 9 × 1.5 = 13.5
Fourth term = Third term × 2.5
? Fourth term = 13.5 × 2.5 = 33.75
Fifth term = Fourth term × 3.5
? Fifth term = 33.75 × 3.5 = 118.125
So 118.125 should come in place of (d).

The given series is in the below pattern,
? First term = 2
Second term = ( First term × 6 ) + 1 = 13
Third term = ( Second term × 5 ) + 2 = 65 , 67 should be sixth term because ( 13 × 5 ) + 2 = 67 .
So 65 is wrong. we get 67 as Third term.
Similarly we can find the all terms
Fourth term = ( Third term × 4 ) + 3 = 271
Fifth term = ( Fourth term × 3 ) + 2 = 817
Sixth term = 1639,
Seventh term = 1645.

The given series is in the below pattern,
First term = 3
Second term = First term x 1 +1³
? Second term = 3 x 1 + 1³ = 3 + 1 = 4
Third term = Second term x 2 + 2³
? Third term = 4 x 2 + 2³ = 8 + 8 = 16
Fourth term = Third term x 3 + 3³
? Fourth term = 16 x 3 + 3³ = 48 + 27 = 75
Fifth term = Fourth term x 4 +4³
? Fifth term = 75 x 4 + 4³ = 300 + 64 = 364
So 366 is wrong. we get 364 as 5th term.
Sixth term = Fifth term x 5 + 5³
? Sixth term = 364 x 5 + 5³ = 1820 + 125 = 1945
Seventh term = Sixth term x 6 + 6³
? Seventh term = 1945 x 6 + 6³ = 11670 + 216 = 11886