Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third number and so on. Which of the given options follows the same set of operations as in the given sets? (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)

I. 16 – 17 – 21 – 30;

II. 13 – 14 – 18 – 27​​

I. 16 – 17 – 21 – 30

II. 13 – 14 – 18 – 27

First number:

Second number = First number +1$$^2$$​​

Third number = Second number + 2 $$^2$$​

Fourth number = Third number +3$$^3$$​​

I. 16 – 17 – 21 – 30     

16   

17 = 16 + 1$$^2$$​​        

21 = 17 + 2​$$^2$$​

30 = 21 + 3$$^2$$​​

II. 13 – 14 – 18 – 27  

13

14 = 13 + 1$$^2$$​​

18 = 14 + 2$$^2$$

27 = 18 + 3²

24

25 = 24 + 1$$^2$$​​

29 = 25 + 2$$^2$$​​

42 $$\neq$$​ 29 + 3$$^2$$​​

42 $$\neq$$​ 39 ( does not follow)

15

16 = 15 + 1$$^2$$​​

20 = 16 + 2$$^2$$​​

26 $$\neq$$​ 20 + 3$$^2$$​​

26 $$\neq$$​ 29 ( does not follow)

11

12 = 11 + 1$$^2$$​​

16 = 12 + 2$$^2$$​​

18 $$\neq$$​ 16 + 3$$^2$$​​

18 $$\neq$$​25 (does not follow)

22

23 = 22 + 1$$^2$$​​

27 = 23 + 2$$^2$$​​

36 = 27 + 3$$^2$$ (Follows)

Thus , the correct answer is option (d) 22 – 23 – 27 – 36