For a given $A.P.$,the first term is $5$ and the $19^{th}$ term is $95$. Then,the sum of its $19$ terms is $\ldots \ldots \ldots \ldots$

Find the sum of all the $11$ terms of an $AP$ whose middle most term is $30$.

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 $Rs.$)

If the sum of the $3^{\text{rd}}$ and the $8^{\text{th}}$ terms of an $AP$ is $7$ and the sum of the $7^{\text{th}}$ and the $14^{\text{th}}$ terms is $-3,$ find the $10^{\text{th}}$ term.

Match the $APs$ given in column $A$ with suitable common differences given in column $B$.

Column $A$	Column $B$
$(A_{1}) \quad 2, -2, -6, -10, \ldots$	$(B_{1}) \quad \frac{2}{3}$
$(A_{2}) \quad a = -18, n = 10, a_{n} = 0$	$(B_{2}) \quad -5$
$(A_{3}) \quad a = 0, a_{10} = 6$	$(B_{3}) \quad 4$
$(A_{4}) \quad a_{2} = 13, a_{4} = 3$	$(B_{4}) \quad -4$
	$(B_{5}) \quad 2$
	$(B_{6}) \quad \frac{1}{2}$
	$(B_{7}) \quad 5$

For an $A.P.$,the $5^{th}$ term is $30$ and the $12^{th}$ term is $100$. Find the sum of the first $20$ terms of the $A.P.$