In an $AP$ given $a=5, d=3, a_{n}=50,$ find $n$ and $S_{n}$.

If the $3^{rd}$ and the $9^{th}$ terms of an $AP$ are $4$ and $-8$ respectively,which term of this $AP$ is zero?

Find the sum of the following $APs$: $0.6, 1.7, 2.8, \ldots,$ to $100$ terms.

$A$ spiral is made up of successive semicircles,with centres alternately at $A$ and $B$,starting with centre at $A$,of radii $0.5 \, cm, 1.0 \, cm, 1.5 \, cm, 2.0 \, cm, \ldots$ as shown in the figure. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take $\pi = \frac{22}{7}$)

For the following $APs$,write the first term and the common difference: $\frac{1}{3}, \frac{5}{3}, \frac{9}{3}, \frac{13}{3}, \ldots$

Find the sum of the following $APs$: $\frac{1}{15}, \frac{1}{12}, \frac{1}{10}, \ldots,$ to $11$ terms.