Question:
Find the $n^{\text {th }}$ term of the AP $8,3,-2,-7,-12, \ldots$
Solution:
To Find: $\mathrm{n}^{\text {th }}$ term of the AP
Given: The series is $8,3,-2,-7,-12, \ldots$
$a_{1}=8, a_{2}=3$ and $d=3-8=-5$
(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: $a_{n}=a+(n-1) d$
$a_{n}=a_{1}+(n-1)(-5)=8-(5 n-5)=8-5 n+5=13-5 n$
So the $n^{\text {th }}$ term of AP is equal to $13-5 n$