Aline in the paschen series of hydrogen has a wavelength of 1010nm. from what state did the electron originate?

N1=3(always) 
wavelength=1010/10^9 m=1.01/10^6 m (converted into metre) 
n2=? 
we have a formula 
1/wavelength= 1.09677x10^7[(1/n1^2)-(1/n2^2)] 
10^6/1.01= 1.01677x10^7[1/9-1/n2^2] 
(9.174x10^5)/(1.09677x10^7)= 1/9-1/n2^2 
0.08365=0.1111-1/n2^2 
1/n2^2=0.1111-0.08365 
n2^2=1/0.02746 
n2=6 

means this electon's ground(original) state was n1=3.After gaining energy it went to n2=6 and when it came back to n1=3,it removed that energy which was seen in the form of spectral lines and these lines had a wavelength of 1010nm. 
the lines are observed in infrared region of the electromagnetic spectrum.

Answer: fn = wcos50 = 38.89(9.81)(cos50) = 245.23 n