The nth term of the sequence 212,1713,119,2023. is - Infinity Learn by Sri Chaitanya

The given sequence can be written as

$\frac{5}{2}, \frac{20}{13}, \frac{10}{9}, \frac{20}{23}, \dots$

The reciprocal of the number

$\frac{8}{20}, \frac{13}{20}, \frac{18}{20}, \frac{23}{20}, \dots$

This is an A.P

$n t h$ term of this A.P. is

$a_{n} = \frac{8 + 5 (n - 1)}{20} = \frac{3 + 5 n}{20}$

Thus, $n t h$ term of the given sequence is

$\frac{20}{5 n + 3}$

The $n t h$ term of the sequence $2 \frac{1}{2}, 1 \frac{7}{13}, 1 \frac{1}{9}, \frac{20}{23} .$ is