If ${a_1} = {a_2} = 2,\;{a_n} = {a_{n - 1}} - 1\;(n > 2)$, then ${a_5}$ is
$1$
$- 1$
$0$
$- 2$
If the $A.M.$ between $p^{th}$ and $q^{th}$ terms of an $A.P.$ is equal to the $A.M.$ between $r^{th}$ and $s^{th}$ terms of the same $A.P.$, then $p + q$ is equal to
If $a_1, a_2, a_3 …………$ an are in $A.P$ and $a_1 + a_4 + a_7 + …………… + a_{16} = 114$, then $a_1 + a_6 + a_{11} + a_{16}$ is equal to
Let $a$, $b$ be two non-zero real numbers. If $p$ and $r$ are the roots of the equation $x ^{2}-8 ax +2 a =0$ and $q$ and $s$ are the roots of the equation $x^{2}+12 b x+6 b$ $=0$, such that $\frac{1}{ p }, \frac{1}{ q }, \frac{1}{ r }, \frac{1}{ s }$ are in A.P., then $a ^{-1}- b ^{-1}$ is equal to $......$
Let $\frac{1}{{{x_1}}},\frac{1}{{{x_2}}},\frac{1}{{{x_3}}},.....,$ $({x_i} \ne \,0\,for\,\,i\, = 1,2,....,n)$ be in $A.P.$ such that $x_1 = 4$ and $x_{21} = 20.$ If $n$ is the least positive integer for which $x_n > 50,$ then $\sum\limits_{i = 1}^n {\left( {\frac{1}{{{x_i}}}} \right)} $ is equal to.
The first term of an $A.P. $ is $2$ and common difference is $4$. The sum of its $40$ terms will be