First slide

Arithmetic progression

Question

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

Moderate

A

$\frac{15}{5 n + 3}$
B

$\frac{20}{5 n + 4}$
C

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

$\frac{20}{5 n + 2}$

Solution

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

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