The first term of an $A.P. $ is $2$ and common difference is $4$. The sum of its $40$ terms will be

If $3^{2 \sin 2 \alpha-1},14$ and $3^{4-2 \sin 2 \alpha}$ are the first three terms of an $A.P.$ for some $\alpha$, then the sixth term of this $A.P.$ is 

Find the $25^{th}$ common term of the following $A.P.'s$

$S_1 = 1, 6, 11, .....$

$S_2 = 3, 7, 11, .....$

Let $a_1 , a_2, a_3, .... , a_n$, be in $A.P$. If $a_3 + a_7 + a_{11} + a_{15} = 72$ , then the sum of its first $17$ terms is equal to

$150$ workers were engaged to finish a piece of work in a certain number of days. $4$ workers dropped the second day, $4$ more workers dropped the third day and so on. It takes eight more days to finish the work now. The number of days in which the work was completed is

Write the first five terms of the following sequence and obtain the corresponding series :

$a_{1}=3, a_{n}=3 a_{n-1}+2$ for all $n\,>\,1$