Question

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

Answer 1

$\frac{1}{2},\frac{1}{6},\frac{1}{18},\frac{1}{54},....,\frac{1}{4374}$

$a=\frac{1}{2},l=\frac{1}{4374},r=\frac{t_n}{t_{n-1}}=\frac{t_2}{t_1}=\frac{\frac{1}{6}}{\frac{1}{2}}=\frac{1}{3}$

$\therefore$ 4th term from the end is

$t_n=l{\left(\frac{1}{r}\right)}^{n-1}$

$t_4=\left(\frac{1}{4374}\right)(3{)}^{n-1}$

$=\frac{1}{4374}\times 3^3$

$=\frac{1}{162}$

$\therefore$ 4th term from the end is $\frac{1}{162}$