If $2, x, 20$ are three consecutive terms of an $A.P.$,then $x = ..........$

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

For a finite $A.P.$,the first term is $2$ and the last term is $50$. If the sum of all the terms is $442$,find the common difference $d$.

The production of a $TV$ factory increases equally every year. Its production in the $3^{rd}$ year was $600 \, TV$ and its production in the $7^{th}$ year was $700 \, TV$. Find the production in the $1^{st}$ year,in the $10^{th}$ year,and the total production in $7$ years.

In each of the following,$a$ and $d$ for an $A.P.$ are given. Find the $A.P.$ in each case. $a=8, d=5$

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