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?

Are $\sqrt{2}, \sqrt{8}, \sqrt{18}, \sqrt{32}, \ldots$ in an $AP$? If they form an $AP$,find the common difference $d$ and write the next three terms.

In which of the following situations,does the list of numbers involved make an arithmetic progression,and why? The amount of money in the account every year,when ₹ $10000$ is deposited at compound interest at $8 \%$ per annum.

The first term of an $AP$ is $5,$ the last term is $45$ and the sum is $400.$ Find the number of terms and the common difference.

Choose the correct choice in the following and justify: the $11^{th}$ term of the $AP: -3, -\frac{1}{2}, 2, \ldots$ is

$-10, -6, -2, 2, \ldots$ are $APs$? If they form an $AP$,find the common difference $d$ and write three more terms.