Find the nth term of each of the following APs:

Solution:

(i)

$5,11,17,23, \ldots$

$a_{n}=a+(n-1) d$

$a=5$

$d=11-5=6$

$a_{n}=5+(n-1) 6$

$a_{n}=6 n-1$

(ii)

$16,9,2,-5$

$a_{n}=a+(n-1) d$

$a=16$

$d=9-16=-7$

$a_{n}=16+(n-1)(-7)$

$a_{n}=16-7 n+7$

$a_{n}=23-7 n$