As per the details in the question the series is in the form of
First series :-
First term = 5
Second term = First term × 1 + 1² = 5 + 1 = 6
Third term = Second term × 2 + 2² = 12 + 4 = 16
similarly , we can calculate the all next terms .
Second series :-
First term = 2
Second term = First term × 1 + 1² = 2 + 1 = 3
Third term = Second term × 2 + 2² = 6 + 4 = 10

Correct Option: E

As per the details in the question the series is in the form of
First series :-
First term = 5
Second term = First term × 1 + 1²
⇒ Second term = 5 × 1 + 1 = 6
Third term = Second term × 2 + 2²
⇒ Third term = 6 × 2 + 4 = 16
similarly , we can find the all others terms .
Second series :-
First term = 2
Second term = First term × 1 + 1²
⇒ Second term = 2 × 1 + 1 = 3
Third term = Second term × 2 + 2²
⇒ Third term = 3 × 2 + 4 = 10
Fourth term = Third term × 3 + 3²
⇒ Fourth term = 10 × 3 + 9 = 39
Fifth term = Fourth term × 4 + 4²
⇒ Fifth term = 39 × 4 + 16 = 172
Hence , the place value of ( d ) is 172 .

The given series is in the below pattern,
First term = 16
Second term = First term + 1² = ?
⇒ Second term = 16 + 1² = 17
∴ ? = 17
Third term = Second term 1² = 15 ;
Similarly , we can calculate all others terms also.

Correct Option: A

The given series is in the below pattern,
First term = 16
Second term = First term + 1²
⇒ Second term = 16 + 1² = 17
∴ ? = 17
Third term = Second term + 2²
⇒ Third term = 17 + 2² = 21
Fourth term = Third term + 3²
⇒ Fourth term = 21 + 3² = 30 ;
Fifth term = Fourth term + 4²
⇒ Fifth term = 30 + 4² = 46 ;
Similarly , we can find all others terms also.
Sixth term = Fifth term + 5²
⇒ Sixth term = 46 + 5² = 71;
Seventh term = Sixth term + 6²
⇒ Sixth term = 71 + 6² = 107
Hence , Second term = 17

The given series is in the below pattern ,
First series :-
First term = 5
Second term = First term × 1 + 4 = 9
Third term = Second term × 2 + 8 = 26
similarly , we can calculate the all next terms .
Second series :-
First term = 13
Second term = First term × 1 + 4 = 17
Third term = Second term × 2 + 8 = 42

Correct Option: E

The given series is in the below pattern ,
First series :-
First term = 5
Second term = First term × 1 + 4
⇒ Second term = 5 × 1 + 4 = 9
Third term = Second term × 2 + 8
⇒ Third term = 9 × 2 + 8 = 26
similarly , we can find the all others terms .
......... and so on .
Second series :-
First term = 13
Second term = First term × 1 + 4
⇒ Second term = 13 × 1 + 4 = 17
Third term = Second term × 2 + 8
⇒ Third term = 17 × 2 + 8 = 42
Fourth term = Third term × 3 + 12
⇒ Fourth term = 42 × 3 + 12 = 138
Fifth term = Fourth term × 4 + 16
⇒ Fifth term = 138 × 4 + 16 = 568
Sixth term = Fifth term × 5 + 20
⇒ Sixth term = 568 × 5 + 20 = 2860
Hence , the place value of ( e ) is 2860 .

As per the details of question is given series in the form of ,
First series :-
First term = 1260
Second term = First term ÷ 2 - 2
⇒ Second term = 1260 ÷ 2 - 2 = 628
Third term = Second term ÷ 2 - 2
⇒ Third term = 628 ÷ 2 - 2 = 312
similarly , we can find the all others terms .
......... and so on .
Second series :-
First term = 788
Second term = First term ÷ 2 - 2 = 392
Third term = Second term ÷ 2 - 2 = 194

Correct Option: B

As per the details of question is given series in the form of ,
First series :-
First term = 1260
Second term = First term ÷ 2 - 2
⇒ Second term = 1260 ÷ 2 - 2 = 628
Third term = Second term ÷ 2 - 2
⇒ Third term = 628 ÷ 2 - 2 = 312
similarly , we can find the all others terms .
......... and so on .
Second series :-
First term = 788
Second term = First term ÷ 2 - 2
⇒ Second term = 788 ÷ 2 - 2 = 392
Third term = Second term ÷ 2 - 2
⇒ Third term = 392 ÷ 2 - 2 = 194
Fourth term = Third term ÷ 2 - 2
⇒ Fourth term = 194 ÷ 2 - 2 = 95
Fifth term = Fourth term ÷ 2 - 2
⇒ Fifth term = 95 ÷ 2 - 2 = 45.5
Hence , the place value of ( d ) is 45.5 .

As per the details in the question the series is in the form of
First term = 4
Second term = First term × 0.5
⇒ Second term = 4 × 0.5 = 2
Third term = Second term × 1.5
⇒ Third term = 2 × 1.5 = ?
∴ ? = 3
Similarly , we can calculate all next terms also.

Correct Option: D

As per the details in the question the series is in the form of
First term = 4
Second term = First term × 0.5
⇒ Second term = 4 × 0.5 = 2
Third term = Second term × 1.5
⇒ Third term = 2 × 1.5 = ?
∴ ? = 3
Fourth term = Third term × 2.5
⇒ Fourth term = 3 × 2.5 = 7.5 ;
Fifth term = Fourth term × 3.5
⇒ Fifth term = 7.5 × 3.5 = 26.25 ;
Similarly , we can find all others terms also.
Sixth term = Fifth term × 4.5
⇒ Sixth term = 26.25 × 4.5 = 118.125;
Hence , Third term = 3