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

If the sum of the first $2n$ terms of $2, 5, 8, \dots$ is equal to the sum of the first $n$ terms of $57, 59, 61, \dots$,then $n$ is equal to

If ${a_1}, {a_2}, {a_3}, \dots, {a_{24}}$ are in arithmetic progression and ${a_1} + {a_5} + {a_{10}} + {a_{15}} + {a_{20}} + {a_{24}} = 225$,then ${a_1} + {a_2} + {a_3} + \dots + {a_{23}} + {a_{24}} = $

If the $9^{th}$ and $19^{th}$ terms of an arithmetic progression are $35$ and $75$ respectively,what is its $20^{th}$ term?

The $p^{\text{th}}$,$q^{\text{th}}$,and $r^{\text{th}}$ terms of an $A.P.$ are $a$,$b$,and $c$ respectively. Show that $(q-r)a + (r-p)b + (p-q)c = 0$.

If the sum and product of the first three terms in an $A.P.$ are $33$ and $1155$,respectively,then a value of its $11^{th}$ term is