Find the indicated terms in each of the following sequences whose nth terms are:
$ a_{n}=\frac{3 n-2}{4 n+5} ; a_{7} $ and $ a_{8} $

Given:

$a_{n}=\frac{3 n-2}{4 n+5}$

To do:

We have to find $a_{7}$ and $a_{8}$.

Solution:

 To find $a_{7}$, we have to substitute $7$ in place of $n$ in $a_{n}=\frac{3 n-2}{4 n+5}$.

This implies,

$a_{7}=\frac{3(7)-2}{4(7)+5}$

$=\frac{21-2}{28+5}$

$=\frac{19}{33}$

 To find $a_{8}$, we have to substitute $8$ in place of $n$ in $a_{n}=\frac{3 n-2}{4 n+5}$.

This implies,

$a_{8}=\frac{3(8)-2}{4(8)+5}$

$=\frac{24-2}{32+5}$

$=\frac{22}{37}$.

Therefore, $a_{7}=\frac{19}{33}$ and $a_{8}=\frac{22}{37}$. 

Tutorialspoint

Updated on: 10-Oct-2022

40 Views

Kickstart Your Career

Get certified by completing the course

Get Started