Question

Find the next term of the sequence:

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

• A. $\frac{1}{168}$
• B. $\frac{1}{164}$
• C. $\frac{1}{162}$
• D. $\frac{1}{170}$

Answer 1

Answer: (C)

$\frac{1}{162}$

The given sequence is $\frac{1}{2},\frac{1}{6},\frac{1}{18},\frac{1}{54},..........$

Here, first term $t_1=a=\frac{1}{2}$

$t_2=\frac{1}{2}{\left(\frac{1}{3}\right)}^1=\frac{1}{6}$
$t_3=\frac{1}{2}{\left(\frac{1}{3}\right)}^2=\frac{1}{18}$
$t_4=\frac{1}{2}{\left(\frac{1}{3}\right)}^3=\frac{1}{54}$

Clearly it is a GP with first term $a=\frac{1}{2}$ and common ratio $r=\frac{1}{3}.$
So, $t_n=a{r}^{n-1}$
$\therefore t_5=\frac{1}{2}{\left(\frac{1}{3}\right)}^4=\frac{1}{162}$
Hence, the answer is $\frac{1}{162}$.