Question

Find the 4th term from the end of the G.P. $$\frac{2}{81}, \frac{2}{27}, \frac{2}{9}, ......., 54$$.

Answer 1

Here the first term $$a = \frac{2}{81}$$, the common ratio $$r = \frac{\frac{2}{27}}{\frac{2}{81}} = 3$$ and the last term $$l = 54$$.

The nth term from the end is $$\frac{l}{r^{(n - 1)}}$$.

So the 4th term from the end is

$$\frac{l}{r^{(4 - 1)}} = \frac{54}{3^3}$$ 

$$= \frac{54}{27}$$

$$= 2$$

So, the 4th term from the end is 2.