Answer :

A)


Given: 2, 2√2, 4….. and an = 128


Here, in the above G.P.


a = 2


Common ratio(r) =


We know that in G.P an = arn-1


an = 2 × (√2)n-1


128 = 2 × (√2)n-1


(√2)n-1 = 128/2 = 64


= 64 ( √x = x1/2)


Apply ln on both sides


We get






n – 1 = 12


n = 13


a13 = 128


B)


Given: √3, 3, 3√3 ….. and an = 729


Here, in the above G.P.


a = √3


Common ratio(r)


We know that in G.P an = arn-1


an = √3 × (√3)n-1


729 = (√2)n


(√2)n = 729


= 729 ( √x = )


Apply ln on both sides


We get






n = 12


a12 = 729


C)


Given: and an =


Here, in the above G.P.


a =


Common ratio(r) = =


We know that in G.P an = arn-1


an =





Apply ln on both sides


We get





n = 9


a9 =


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