The series + (1)², + (3)², + (5)², + (7)², + (9)², + (11)². Correct answer 171.

The series is x 1 + (1)², x 2 + (2)², x 3 + (3)², x 4 + (4)², x 5 + (5)², x 6 + (6)².

As per the details in the question the series is in the form of
First term = 2
Second term = First term × 3 + 5
? Second term = 2 × 3 + 5 = 11
Third term = Second term × 4 - 6
? Third term = 11 × 3 + 5 = 38
Fourth term = Third term × 5 + 7
? Fourth term = 38 × 5 + 7 = 197 ;
Fifth term = Fourth term × 6 - 8
? Fifth term = 197 × 6 - 8 = ?
? ? = 1174
Similarly , we can find all others terms also.
Sixth term = Fifth term × 7 + 9
? Sixth term = 1174 × 7 + 9 = 8227;
Seventh term = Sixth term × 8 - 10
? Sixth term = 1174 × 8 - 10 = 65806
Hence , Fifth term = 1174

As per the details in the question the series is in the form of
First term + Second term = Third term
? 7 + 9 = 16;
Second term + Third term = Fourth term
? 9 + 16 = 25;
Similarly , we can find all others terms also.
Third term + Fourth term = Fifth term
? 16 + 25 = 41;
Fourth term + Fifth term = Sixth term
? 25 + 41 = ?
? ? = 66
Fifth term + Sixth term = Seventh term
? 41 + 66 = 107
Sixth term + Seventh term = Eighth term
? 66 + 107 = 173
Hence , Sixth term = 66

The given series is in the below pattern,
First term = 16
Second term = First term × 0.25
? Second term = 16 × 0.25 = 4
Third term = Second term × 0.50
? Third term = 4 × 0.50 = 2
Fourth term = Third term × 0.75
? Fourth term = 2 × 0.75 = 1.5
Fifth term = Fourth term × 1
? Fifth term = 1.5 × 1 = 1.5 ;
? ? = 1.5
Similarly , we can find all others terms also.
Sixth term = Fifth term × 1.25
? Sixth term = 1.5 × 1.25 = 1.875
Hence , Fourth term = 3

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

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
? 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
? 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 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 .