The sum of $1 + 3 + 5 + 7 + \dots$ up to $n$ terms is

In an $A.P.$,the first term is $2$ and the sum of the first five terms is one-fourth of the next five terms. Show that the $20^{th}$ term is $-112$.

If the roots $\alpha, \beta, \gamma$ of the equation $x^3-6x^2+px+10=0$ are in arithmetic progression,then $\alpha^3+\beta^3+\gamma^3=$

If the four angles of a quadrilateral are in an arithmetic progression and their common difference is $10^{\circ}$,what are the measures of the angles of the quadrilateral?

If the sum of the series $20 + 19 \frac{3}{5} + 19 \frac{1}{5} + 18 \frac{4}{5} + \ldots$ up to $n^{\text{th}}$ term is $488$ and the $n^{\text{th}}$ term is negative,then:

If the roots of the equation $x^3+ax^2+bx+c=0$ are in arithmetic progression,then