If $\sum_{n = 1}^5 \frac{1}{n(n + 1)(n + 2)(n + 3)} = \frac{k}{3}$,then $k$ is equal to

Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball,the second row consists of two balls and so on. If $99$ more identical balls are added to the total number of balls used in forming the equilateral triangle,then all these balls can be arranged in a square whose each side contains exactly $2$ balls less than the number of balls each side of the triangle contains. Then the number of balls used to form the equilateral triangle is

Consider an infinite $G.P.$ with first term $a$ and common ratio $r$. If its sum is $4$ and the second term is $3/4$,then:

$150$ workers were engaged to finish a piece of work in a certain number of days. $4$ workers dropped out on the second day,$4$ more workers dropped out on the third day,and so on. It takes $8$ more days to finish the work now. The number of days in which the work was completed is:

The first term of a $G.P.$ whose second term is $2$ and sum to infinity is $8$,will be

If the $7^{th}$ term of a $H.P.$ is $\frac{1}{10}$ and the $12^{th}$ term is $\frac{1}{25}$,then the $20^{th}$ term is