If the first, second and last terms of an $A.P.$ be $a,\;b,\;2a$ respectively, then its sum will be
$\frac{{ab}}{{b - a}}$
$\frac{{ab}}{{2(b - a)}}$
$\frac{{3ab}}{{2(b - a)}}$
$\frac{{3ab}}{{4(b - a)}}$
${7^{th}}$ term of an $A.P.$ is $40$, then the sum of first $13$ terms is
A man starts repaying a loan as first instalment of $Rs.$ $100 .$ If he increases the instalment by $Rs \,5$ every month, what amount he will pay in the $30^{\text {th }}$ instalment?
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 :
Given that $n$ A.M.'s are inserted between two sets of numbers $a,\;2b$and $2a,\;b$, where $a,\;b \in R$. Suppose further that ${m^{th}}$ mean between these sets of numbers is same, then the ratio $a:b$ equals
Find the sum of all natural numbers lying between $100$ and $1000,$ which are multiples of $5 .$