Ramkali saved ₹ $5$ in the first week of a year and then increased her weekly savings by ₹ $1.75$. If in the $n$-th week,her weekly savings become ₹ $20.75$,find $n$.

An $AP$ consists of $50$ terms of which the $3^{rd}$ term is $12$ and the last term is $106$. Find the $29^{th}$ term.

$A$ sum of ₹ $700$ is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is ₹ $20$ less than its preceding prize,find the value of each of the prizes.

Do $4, 10, 16, 22, \ldots$ form an $AP$? If they form an $AP,$ write the next two terms.

Two $APs$ have the same common difference. The difference between their $100^{th}$ terms is $100$. What is the difference between their $1000^{th}$ terms?

Are $a, a^{2}, a^{3}, a^{4}, \ldots$ in an $AP$? If they form an $AP$,find the common difference $d$ and write three more terms.