Find the 4th term from the end of the G.P.

Question:

Find the 4 th term from the end of the G.P. $\frac{1}{2}, \frac{1}{6}, \frac{1}{18}, \frac{1}{54}, \ldots, \frac{1}{4374}$

Solution:

After reversing the given G.P., we get another G.P. whose first term, $l$ is $\frac{1}{4374}$ and common ratio is 3 .

$\therefore 4^{\text {th }}$ term from the end $=l\left(\frac{1}{r}\right)^{4-1}$

$=\left(\frac{1}{4374}\right)(3)^{4-1}$

$=\left(\frac{27}{4374}\right)$

$=\frac{1}{162}$

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