Question:
Find the $23^{\text {rd }}$ term of the AP $7,3,1,-1,-3, \ldots$
Solution:
To Find: $23^{\text {rd }}$ term of the AP
Given: The series is $7,5,3,1,-1,-3, \ldots$
$a_{1}=7, a_{2}=5$ and $d=3-5=-2$
(Where $a=a_{1}$ is first term, $a_{2}$ is second term, $a_{n}$ is nth term and $d$ is common difference of given $A P$ )
Formula Used: $a_{n}=a+(n-1) d$
So put n =23 in above formula, we have
$a_{23}=a_{1}+(23-1)(-2)=7-44=-37$
So $23^{\text {rd }}$ term of AP is equal to $-37$.