Answer:
![a_110=41+(110-1)4](https://tex.z-dn.net/?f=a_110%3D41%2B%28110-1%294)
Step-by-step explanation:
He already has songs = 41
Since we are given that he purchase four songs every week .
So, in first week he purchase songs = 4
Initially he already has 41 songs
So, total songs after 1 week = ![41+(4\times1)=45](https://tex.z-dn.net/?f=41%2B%284%5Ctimes1%29%3D45)
After 2 weeks he will have songs = ![41+(4\times 2)=49](https://tex.z-dn.net/?f=41%2B%284%5Ctimes%202%29%3D49)
This forms an arithmetic sequence : 41,45,49......
Formula of nth term in A.P. : ![a_n=a+(n-1)d](https://tex.z-dn.net/?f=a_n%3Da%2B%28n-1%29d)
a = first term = 41
d = common difference = 45-41=49-45=4
Since we are required to find the new songs after110 weeks
So, n =110
Substituting values :
![a_110=41+(110-1)4](https://tex.z-dn.net/?f=a_110%3D41%2B%28110-1%294)
Thus Option A is correct.