What is the sum of all two digit numbers which give a remainder of $4$ when divided by $6$ ?

If $a,\;b,\;c$ are in $A.P.$, then $\frac{{{{(a - c)}^2}}}{{({b^2} - ac)}} = $

If the ${n^{th}}$ term of an $A.P.$ be $(2n - 1)$, then the sum of its first $n$ terms will be

Write the first five terms of the sequences whose $n^{t h}$ term is $a_{n}=(-1)^{n-1} 5^{n+1}$

Let $a_1, a_2, a_3, \ldots$ be in an arithmetic progression of positive terms.

Let $\mathrm{A}_{\mathrm{k}}=\mathrm{a}_1{ }^2-\mathrm{a}_2{ }^2+\mathrm{a}_3{ }^2-\mathrm{a}_4{ }^2+\ldots+\mathrm{a}_{2 \mathrm{k}-1}{ }^2-\mathrm{a}_{2 \mathrm{k}}{ }^2$.

If $\mathrm{A}_3=-153, \mathrm{~A}_5=-435$ and $\mathrm{a}_1{ }^2+\mathrm{a}_2{ }^2+\mathrm{a}_3{ }^2=66$, then $\mathrm{a}_{17}-\mathrm{A}_7$ 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.