The first and the last terms of an $AP$ are $17$ and $350$ respectively. If the common difference is $9,$ how many terms are there and what is their sum?

$A$ manufacturer of $TV$ sets produced $600$ sets in the third year and $700$ sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year,find the total production in first $7$ years.

Find the sum of the first $24$ terms of the list of numbers whose $n^{th}$ term is given by $a_{n} = 3 + 2n$.

The taxi fare after each $km$ when the fare is ₹ $15$ for the first $km$ and ₹ $8$ for each additional $km$. Does the list of numbers involved form an arithmetic progression,and why?

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?

Find the sum given below: $-5 + (-8) + (-11) + \ldots + (-230)$