Find the sum of the series: $7 + 10 \frac{1}{2} + 14 + \ldots + 84$.

If $7$ times the $7^{\text{th}}$ term of an $AP$ is equal to $11$ times its $11^{\text{th}}$ term,then its $18^{\text{th}}$ term will be

The taxi fare after each $km$,when the fare is $Rs. 15$ for the first $km$ and $Rs. 8$ for each additional $km$,does not form an $AP$ as the total fare (in $Rs.$) after each $km$ is $15, 8, 8, 8, \ldots$. Is the statement true? Give reasons.

The sum of three numbers in $A.P.$ is $12$ and the sum of their cubes is $288$. Find those numbers.

Find the sum of the two middle most terms of the $AP: -\frac{4}{3}, -1, -\frac{2}{3}, \ldots, 4 \frac{1}{3}$.

Kanika was given her pocket money on Jan $1^{\text{st}}, 2008$. She puts $Rs.\, 1$ on Day $1$,$Rs.\, 2$ on Day $2$,$Rs.\, 3$ on Day $3$,and continued doing so till the end of the month,from this money into her piggy bank. She also spent $Rs.\, 204$ of her pocket money,and found that at the end of the month she still had $Rs.\, 100$ with her. How much was her pocket money for the month? (in $Rs.$)