The 6th term from the end of the sequence 4, 8, 16, 32,.....,16384 is .

1024

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512

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256

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Solution

The correct option is B 512
The given sequence 4, 8, 16, 32,.....,16384 is clearly a GP with first term 4 and common ratio r=2.
The 6th terms from end of the given GP will be the 6th term from beginning of the GP formed by reversing the order of the terms of the given GP.
16384,.....,32, 16, 8, 4
Here a=16384 and r = 1/2.
$a_{n} = a r^{n - 1} \Rightarrow a_{6} = 16384 {(\frac{1}{2})}^{6 - 1} \Rightarrow a_{6} = 16384 \times \frac{1}{32} \Rightarrow a_{6} = 512$
$∴ 6 th$ term from the end of the given G.P. is $512$

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