The sum of the series $\frac{1}{2} + \frac{1}{3} + \frac{1}{6} + ........$ to $9$ terms is
If the roots of the equation $x^3 - 9x^2 + \alpha x - 15 = 0 $ are in $A.P.$, then $\alpha$ is
Insert $6$ numbers between $3$ and $24$ such that the resulting sequence is an $A.P.$
When $9^{th}$ term of $A.P$ is divided by its $2^{nd}$ term then quotient is $5$ and when $13^{th}$ term is divided by $6^{th}$ term then quotient is $2$ and Remainder is $5$ then find first term of $A.P.$
What is the $20^{\text {th }}$ term of the sequence defined by
$a_{n}=(n-1)(2-n)(3+n) ?$