We can see from points
(2,1) means for n = 2, a = 1
(3,3) means for n = 3, a = 3
(4,9) means for n = 4 , a= 9
Now try to see relation in outputs 1,3,9.
We can write 1 as ![3^{0}](https://tex.z-dn.net/?f=%203%5E%7B0%7D%20%20)
3 as ![3^{1}](https://tex.z-dn.net/?f=%203%5E%7B1%7D%20%20)
9 as ![3^{2}](https://tex.z-dn.net/?f=%203%5E%7B2%7D%20%20)
So (2,2) would mean for n =2, a = 1 or
----------------(1)
(3,3) would mean for n = 3, a = 3 or
-------------(2)
(4,9) would mean for n = 4, a = 9 or
--------------------(3)
From (1) we can see for n =2, exponent on 3 is 0
From (2) we can see for n =3, exponent on 3 is 1
From (3) we can see for n =4, exponent on 3 is 2
So we can see the pattern whatever is n value its 2 less is the exponent on 3. So for n exponent on 3 will be n-2
For n = n, a = ![3^{n-2}](https://tex.z-dn.net/?f=%203%5E%7Bn-2%7D%20%20)
Now looking at options given
option (A)
doesnt match to ![3^{n-2}](https://tex.z-dn.net/?f=%203%5E%7Bn-2%7D%20%20)
so its incorrect
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option (B)
doesnt match to ![3^{n-2}](https://tex.z-dn.net/?f=%203%5E%7Bn-2%7D%20%20)
so its incorrect
----------------------------------------------------------------------------------------------------------
option (B)
which we can also write as
![\frac{3^{n-1}}{3} = \frac{3^{n-1}}{3^{1}} = 3^{n-1-1} = 3^{n-2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%5E%7Bn-1%7D%7D%7B3%7D%20%20%3D%20%5Cfrac%7B3%5E%7Bn-1%7D%7D%7B3%5E%7B1%7D%7D%20%20%3D%203%5E%7Bn-1-1%7D%20%20%3D%203%5E%7Bn-2%7D%20%20)
we subtract exponents when dividing same bases so we subtracted exponent 1 from n-1 and finally got ![3^{n-2}](https://tex.z-dn.net/?f=%203%5E%7Bn-2%7D%20%20)
so option (c) matches and is right answer
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option (D)
doesnt match to ![3^{n-2}](https://tex.z-dn.net/?f=%203%5E%7Bn-2%7D%20%20)
so its incorrect