If $a_1, a_2, a_3, …….$ are in $A.P.$ such that $a_1 + a_7 + a_{16} = 40$, then the sum of the first $15$ terms of this $A.P.$ is
$200$
$280$
$150$
$120$
The number of common terms in the progressions $4,9,14,19, \ldots \ldots$, up to $25^{\text {th }}$ term and $3,6,9,12$, up to $37^{\text {th }}$ term is :
The $A.M.$ of a $50$ set of numbers is $38$. If two numbers of the set, namely $55$ and $45$ are discarded, the $A.M.$ of the remaining set of numbers is
If $a_m$ denotes the mth term of an $A.P.$ then $a_m$ =
If the first term of an $A.P. $ be $10$, last term is $50$ and the sum of all the terms is $300$, then the number of terms are
If the sum of $\mathrm{n}$ terms of an $\mathrm{A.P.}$ is $n P+\frac{1}{2} n(n-1) Q,$ where $\mathrm{P}$ and $\mathrm{Q}$ are constants, find the common difference.