Question:
Find the nth term of each of the following APs:
(i) 5, 11, 17, 23, ....
(ii) 16, 9, 2, –5, ....
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)
$16,9,2,-5$
$a_{n}=a+(n-1) d$
$a=16$
$d=9-16=-7$
$a_{n}=16+(n-1)(-7)$
$a_{n}=16-7 n+7$
$a_{n}=23-7 n$