If $^n{C_4},{\,^n}{C_5},$ and ${\,^n}{C_6},$ are in $A.P.,$ then $n$ can be
$9$
$14$
$11$
$12$
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.
Write the first five terms of the sequences whose $n^{t h}$ term is $a_{n}=\frac{2 n-3}{6}$
The number of terms of the $A.P. 3,7,11,15...$ to be taken so that the sum is $406$ is
If $a,b,c,d,e$ are in $A.P.$ then the value of $a + b + 4c$ $ - 4d + e$ in terms of $a$, if possible is
If the sum of $n$ terms of an $A.P.$ is $3 n^{2}+5 n$ and its $m^{\text {th }}$ term is $164,$ find the value of $m$