Question

Find the nth term of each of the following APs:
(i) 5, 11, 17, 23, ....
(ii) 16, 9, 2, –5, ....

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right) \\ 5,11,17,23,... \\ {a}_n=a+\left(n-1\right)d \\ a=5 \\ d=11-5=6 \\ {a}_n=5+\left(n-1\right)6 \\ {a}_n=6n-1 \end{gathered}$$

$$\begin{gathered} \left(\mathrm{ii}\right) \\ 16,9,2,-5 \\ {a}_n=a+\left(n-1\right)d \\ a=16 \\ d=9-16=-7 \\ {a}_n=16+\left(n-1\right)\left(-7\right) \\ {a}_n=16-7n+7 \\ {a}_n=23-7n \end{gathered}$$