If the sum of $n$ terms of an $A.P$. is $2{n^2} + 5n$, then the ${n^{th}}$ term will be

If the $9^{th}$ term of an $A.P.$ be zero, then the ratio of its $29^{th}$ and $19^{th}$ term is

Let the sequence ${a_1},{a_2},{a_3},.............{a_{2n}}$ form an $A.P. $ Then $a_1^2 - a_2^2 + a_3^3 - ......... + a_{2n - 1}^2 - a_{2n}^2 = $

Three number are in $A.P.$ such that their sum is $18$ and sum of their squares is $158$. The greatest number among them is

Given sum of the first $n$ terms of an $A.P.$ is $2n + 3n^2.$ Another $A.P.$ is formed with the same first term and double of the common difference, the sum of $n$ terms of the new $A.P.$ is

If $\log _e \mathrm{a}, \log _e \mathrm{~b}, \log _e \mathrm{c}$ are in an $A.P.$ and $\log _e \mathrm{a}-$ $\log _e 2 b, \log _e 2 b-\log _e 3 c, \log _e 3 c-\log _e a$ are also in an $A.P,$ then $a: b: c$ is equal to