If twice the $11^{th}$ term of an $A.P.$ is equal to $7$ times of its $21^{st}$ term, then its $25^{th}$ term is equal to
$24$
$120$
$0$
None of these
Maximum value of sum of arithmetic progression $50, 48, 46, 44 ........$ is :-
If ${a_1} = {a_2} = 2,\;{a_n} = {a_{n - 1}} - 1\;(n > 2)$, then ${a_5}$ is
Which term of the sequence $( - 8 + 18i),\,( - 6 + 15i),$ $( - 4 + 12i)$ $,......$ is purely imaginary
The sum of the common terms of the following three arithmetic progressions.
$3,7,11,15,...................,399$
$2,5,8,11,............,359$ and
$2,7,12,17,...........,197$, is equal to $................$.
The $p^{\text {th }}, q^{\text {th }}$ and $r^{\text {th }}$ terms of an $A.P.$ are $a, b, c,$ respectively. Show that $(q-r) a+(r-p) b+(p-q) c=0$