If the ratio of the $$7th$$ term from the beginning to the $$7th$$ term from the end in the expansion of $$21/3+3$$−$$1/3n$$ is $$1/6$$ then the value of n is

Question

If the ratio of the $$7th$$ term from the beginning to the $$7th$$ term from the end in the expansion of $$21/3+3$$−$$1/3n$$  is  $$1/6$$ then the value of n is

Infinity Learn · Accepted Answer

Let  $$a=7th$$ term from the $$beginning=T7=T6+1=nC621/3n$$−$$63$$−$$1/36and$$ let $$b=7th$$ term from the $$end=(n+2$$−$$7)$$ th or (n$$−$$5) th  term from the $$beginning=nCn$$−$$621/3n$$−$$(n$$−$$6)3$$−$$1/3n$$−$$6=nC621/363$$−$$1/3n$$−$$6we$$ are given $$ab=1621/3n$$−$$63$$−$$1/3621/363$$−$$1/3n$$−$$6=16$$⇒$$21/33$$−$$1/3n$$−$$12=16$$⇒$$6(n$$−$$12)/3=6$$−$$1$$⇒n−$$12=$$−$$3$$⇒$$n=9$$.

If the ratio of the 7th term from the beginning to the 7th term from the end in the expansion of $(2^{1 / 3} +$ ${3^{- 1 / 3})}^{n}$ is $1 / 6$ then the value of $n$ is

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If the ratio of the 7th term from the beginning to the 7th term from the end in the expansion of 21/3+3−1/3n is 1/6 then the value of n is

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If the ratio of the 7th term from the beginning to the 7th term from the end in the expansion of $(2^{1 / 3} +$ ${3^{- 1 / 3})}^{n}$ is $1 / 6$ then the value of $n$ is