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  4. Find 4th term from the end of the G.P. 3, 6, 12, 24., .........., 3072.

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Q. Find $4^{th}$ term from the end of the G.P. 3, 6, 12, 24., .........., 3072.

Sequences and Series

Solution:

Clearly, the given progression is a G.P. with common ratio r = 2.
$\therefore \, 4^{th}$ term from the end $ = \ell \left( \frac{1}{r} \right)^{4-1}$
$ = (3072) \left( \frac{1}{2} \right)^{4-1} = 384$