Find the 4th term from the end of the GP.

The given GP is . (1)


The first term in the GP,


The second term in the GP,


The common ratio,r = 3


The last term in the given GP is an = 162.


Second last term in the GP = an-1 = arn-2


Starting from the end, the series forms another GP in the form,


arn-1, arn-2, arn-3….ar3, ar2, ar, a (2)


Common ratio of this GP is .


So,.


So, 4th term of the GP (2),


a4 = ar3


=


Hence, the 4th term from the end of the given GP is 6.


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