Q. 133.7( 3 Votes )

# Find the 4^{th} term from the end of the GP.

Answer :

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 a_{n} = 162.

Second last term in the GP = a_{n-1} = ar^{n-2}

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

ar^{n-1}, ar^{n-2}, ar^{n-3}….ar^{3}, ar^{2}, ar, a → (2)

Common ratio of this GP is .

So,.

So, 4^{th} term of the GP (2),

a_{4} = ar^{3}

=

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

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