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

Maximum value of the sum of the arithmetic progression $50, 48, 46, 44, \dots$ is:

If the sum of the $10$ terms of an $A.P.$ is $4$ times the sum of its $5$ terms,then the ratio of the first term to the common difference is:

If the sum of $n$ terms of an $AP$ is given by $S_{n} = n^{2} + n$,then the common difference of the $AP$ is

If the sum of two extreme numbers of an $A.P.$ with four terms is $8$ and the product of the remaining two middle terms is $15$,then the greatest number of the series will be:

$150$ 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