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

a = $\dfrac{2}{81}$

r = $\dfrac{\dfrac{2}{27}}{\dfrac{2}{81}} = 3$

l = 54

We know that,

nth term from end of a G.P. is given by,

T_n = $\dfrac{l}{r^{n - 1}}$

$\Rightarrow \text{4th from end}= \dfrac{54}{3^{4-1}} \\[1em] = \dfrac{54}{3^{3}} \\[1em] = \dfrac{54}{27} \\[1em] = 2.$

Hence, 4th term from end = 2.