From the given graph , we can see that the increasing order of series as -
First term = 2
Second term = First term + 2² = 8
Third term = Second term + 3² = 32
Similarly , we can calculate all others terms also.

Correct Option: D

From the given graph , we can see that the increasing order of series as -
First term = 2
Second term = First term × 2 + 2²
⇒ Second term = 2 × 2 + 2² = 4 + 4 = 8 ;
Third term = Second term × 3 + 3²
⇒ Third term = 8 × 3 + 3² = 24 + 9 = 32 ; 32 is wrong. It should be 33.
Similarly , we can find all others terms also.
Fourth term = Third term × 4 + 4²
⇒ Fourth term = 33 × 4 + 4² = 132 + 16 = 148 ;
Fifth term = Fourth term × 5 + 5²
⇒ Fifth term = 148 × 5 + 5² = 740 + 25 = 765 ;
Sixth term = Fifth term × 6 + 6²
⇒ Sixth term = 765 × 6 + 6² = 4590 + 36 = 4626 ;
Seventh term = Sixth term × 7 + 7²
⇒ Seventh term = 4626 × 7 + 7² = 32382 + 49 = 32431
Hence, 32 is wrong. It should be 33.

The given series is in the below pattern,we can see that
Next term = Previous term ÷ n { putting n = 2 and 1.5 alternately }
First term = 108
Second term = First term ÷ 2
⇒ Second term = 108 ÷ 2 = 54 ;
Third term = Second term ÷ 1.5
⇒ Third term = 54 ÷ 1.5 = 36 ;
Similarly , we can calculate all others terms also.

Correct Option: D

The given series is in the below pattern,we can see that
Next term = Previous term ÷ n { putting n = 2 and 1.5 alternately }
First term = 108
Second term = First term ÷ 2
⇒ Second term = 108 ÷ 2 = 54 ;
Third term = Second term ÷ 1.5
⇒ Third term = 54 ÷ 1.5 = 36 ;
Third term = Third term ÷ 2
⇒ Fourth term = 36 ÷ 2 = 18 ;
Fifth term = Fourth term ÷ 1.5
⇒ Fifth term = 18 ÷ 1.5 = 9 is wrong. It should be 12.
Sixth term = Fifth term ÷ 2
⇒ Sixth term = 12 ÷ 2 = 6 ;
Seventh term = Sixth term ÷ 1.5
⇒ Seventh term = 8 ÷ 1.5 = 4
Hence, 9 is wrong. It should be 12.

From above given series , we can see that
The differences are given as -
Second term - First term = 1– 0 = 1 = 1³;
Third term - Second term = 9 – 1= 8 = 2³;
Similarly , we can calculate all others terms also.

Correct Option: C

From above given series , we can see that
The differences are given as -
Second term - First term = 1– 0 = 1 = 1³;
Third term - Second term = 9 – 1= 8 = 2³;
Similarly , we can find all others terms also.
Fourth term - Third term = 36 – 9 = 27 = 3³;
Fifth term - Fourth term = 99 – 36 = 63 ≠ 4 ³
But , Fifth term - Fourth term = 100 – 36 = 64 = 4³;
Here , fifth term 99 is wrong , it should be 100 as fifth term .
Sixth term - Fifth term = 225 – 100 = 125 = 5³;
Seventh term - Sixth term = 441– 225 = 216 = 6³

As per the details in the question the series is in the form of
First term = 2
Second term = First term × 1.5 = 3
Third term = Second term × 2 = 6
Similarly , we can calculate all next terms also.

Correct Option: E

As per the details in the question the series is in the form of
First term = 2
Second term = First term × 1.5
⇒ Second term = 2 × 1.5 = 3 ;
Third term = Second term × 2
⇒ Third term = 3 × 2 = 6 ;
Similarly , we can find all others terms also.
Fourth term = Third term × 2.5 = 6 × 2.5 = 15 ;
Fifth term = Fourth term × 3 = 15 × 3 = 45 ;
Sixth term = Fifth term × 3.5 = 45 × 3.5 =156.5; 156.5 is wrong. It should be 157.5 .
Seventh term = Sixth term × 4 =157.5 × 4 = 630
Hence, 156.5 is wrong. It should be 157.5.