Which term of the $A.P.$ $4, 9, 14, \ldots$ is $224$ (in $^{th}$)?

In an $A.P.$,ten times the $10^{th}$ term equals fifteen times the $15^{th}$ term. Prove that the $25^{th}$ term of the $A.P.$ is $0$.

For the $A.P.$ $\frac{3}{2}, \frac{7}{2}, \frac{11}{2}, \frac{15}{2}, \ldots,$ the common difference is

$A$ person has to clear a debt of $Rs. 3250$ by monthly instalments. In the first month he has to pay $Rs. 20$ and then onwards every instalment is $Rs. 15$ more than the previous instalment. How long will it take to clear the debt?

Find the sum of multiples of $5$ lying between $84$ and $719$.

If the sum of the first $6$ terms of an $AP$ is $36$ and that of the first $16$ terms is $256,$ find the sum of the first $10$ terms.