The given series is in the below pattern,we can see that
Next term= ( Previous term × variable ) + variable
First term = 3
Second term = ( First term × variable ) + 0.5 = ( 3 x 0.5 ) + 0.5 = 2
Third term = ( Second term × variable ) + 1 = ( 2 x 1 ) + 1 = 3
Similarly , we can calculate all others terms also.

Correct Option: E

The given series is in the below pattern,we can see that
Next term= ( Previous term × variable ) + variable
First term = 3
Second term = ( First term × variable ) + 0.5 = ( 3 x 0.5 ) + 0.5 = 2
Third term = ( Second term × variable ) + 1 = ( 2 x 1 ) + 1 = 3
Similarly , we can calculate all others terms also.
Fourth term = ( Third term × variable ) + 1.5 = ( 3 × 1.5 ) + 1.5 = 6 ;
Fifth term = ( Fourth term × variable ) + 2 = ( 6 × 2 ) + 2 = 12 ; 12 is wrong. It should be 14.
Sixth term = ( Fifth term × variable ) + 2.5 = (14 × 2.5 ) + 2.5 = 37.5 ;
Seventh term = ( Sixth term × variable ) + 3 = ( 37.5 × 3 ) + 3 = 115.5
Hence, 12 is wrong. It should be 14.

The given series is in the below pattern,
First term = 2
Second term = First term + 1³ = 3
Third term = Second term + 2³ = 11
Similarly , we can calculate all others terms also.

Correct Option: B

The given series is in the below pattern,
First term = 2
Second term = First term + 1³
⇒ Second term = 2 + 1³ = 3 ;
Third term = Second term + 2³
⇒ Third term = 3 + 2³ = 11 ;
Similarly , we can find the all others terms also.
Fourth term = Third term + 4²
⇒ Fourth term = 11 + 3³ = 38 ;
Fifth term = Fourth term + 5²
⇒ Fifth term = 38 + 4³ = 102
Sixth term = Fifth term + 6²
⇒ Sixth term = 102 + 5³ = 229 ; 229 is wrong. It should be 227.
Seventh term = Sixth term + 7²
⇒ Seventh term = 227 + 6³ = 443
Hence, 229 is wrong. It should be 227.

From the given figure , we can see that
First term = 2807
Second term = ( First term - 7 ) ÷ 2 = 1400
Third term = ( Second term - 6 ) ÷ 2 = 697

Correct Option: B

From the given figure , we can see that
First term = 2807
Second term = ( First term - 7 ) ÷ 2 = 1400
Third term = ( Second term - 6 ) ÷ 2 = 697
⇒ Second term = ( 2807 - 7 ) ÷ 2 = 1400 ;
⇒ Third term = ( 1400 - 6 ) ÷ 2 = 697 ;
⇒ Fourth term = ( 697 - 5 ) ÷ 2 = 347; 347 is wrong. It should be 346.
⇒ Fifth term = ( 346 - 4 ) ÷ 2 = 171 ;
⇒ Sixth term = ( 171 - 3 ) ÷ 2 = 84 ;
⇒ Seventh term = ( 84 - 2 ) ÷ 2 = 41 ;
⇒ Eighth term = ( 41 - 1 ) ÷ 2 = 20
Hence, 347 is wrong. It should be 346.

The series is an alternate series, having
Next term = ( Previous term × 3 ) - 1
Odd position series :-
First term = 2
Third term = ( First term × 3 ) - 1
.........................and so on .
Even position series :-
Second term = 3
Fourth term = ( Second term × 3 ) - 1
.........................and so on .

Correct Option: E

The series is an alternate series, having
Odd position series :-
First term = 2
Third term = ( First term × 3 ) - 1
⇒ Third term = ( 2 × 3 ) - 1 = 5 ;
Fifth term = ( Third term × 3 ) - 1
⇒ Fifth term = ( 5 × 3 ) - 1 = 14 ;
Seventh term = ( Fifth term × 3 ) - 1
⇒Seventh term = ( 14 × 3 ) - 1 = 41 ;
Even position series :-
Second term = 3
Fourth term = ( Second term × 3 ) - 1
⇒ Fourth term = ( 3 × 3 ) - 1 = 8 ;
Sixth term = ( Fourth term × 3 ) - 1
⇒ Sixth term = ( 8 × 3 ) - 1 = 23 ;
Eighth term = ( Sixth term × 3 ) - 1
⇒ Eighth term = ( 23 × 3 ) - 1 = 69; 69 is wrong. It should be 68.

The given series is in the below pattern,
First term = 3
Second term = First term × 2.5 = 7.5 ;
Third term = Second term × 2 = 15 ;
Similarly , we can calculate all others terms also.

Correct Option: A

The given series is in the below pattern,
First term = 3
Second term = First term × 2.5
⇒ Second term = 3 × 2.5 = 7.5 ;
Third term = Second term × 2
⇒ Third term = 7.5 × 2 = 15 ;
Fourth term = Third term × 2.5
⇒ Fourth term = 15 × 2.5 = 37.5 ;
Fifth term = Fourth term × 2
⇒ Fifth term = 37.5 × 2 = 75 ;
Sixth term = Fifth term × 2.5
⇒ Sixth term = 75 × 2.5 = 167.5; 167.5 is wrong. It should be 187.5.
Seventh term = Sixth term × 2
⇒ Seventh term = 187.5 × 2 = 375 ;
Hence, 167.5 is wrong. It should be 187.5.