If the numbers $n-2, 4n-1$ and $5n+2$ are in $AP$,find the value of $n$.

Solve the equation $-4 + (-1) + 2 + \ldots + x = 437$.

Which term of the $A.P.$ $13, 20, 27, 34, \ldots$ is $384$ (in $^{th}$)?

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

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

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 $Rs.$)

The $26^{\text{th}}$,$11^{\text{th}}$,and the last term of an $AP$ are $0$,$3$,and $-\frac{1}{5}$,respectively. Find the common difference and the number of terms.