I believe the answer is 2 :) .
There are 7 keys in each octave (C,D,E,F,G,A and B) so it would make sense to divide 52 to 7.
52/7=7 octaves and 3 extra kets
Here, Sequence : -2, -6, -18, -54
Common Ratio = a₂/a₁ = -6/-2 = 3
As the expression is in negative sign, it's sequence will be -3ˣ
Where x = number of terms in the sequence [ By this rule, you can calculate the unknown nth number]
In short, Option C is your answer!!!!
Let me know, if you have some doubt.
From my notes I’ve the derivative of arctan(x)= 1/(1+x^2)