JIPMAT (QA) PYQs

If the $m^{\text{th}}$ term of an arithmetic progression is $\frac{1}{n}$ and the $n^{\text{th}}$ term is $\frac{1}{m}$, then the $mn^{\text{th}}$ term of this progression will be

Assertion [A]: Sum of the first hundred even natural numbers divisible by 5 is 45050.
Reason (R): Sum of the first n-terms of an Arithmetic Progression is given by $S = (n/2) *(a + l)$ where a=first term, l=last term.
Choose the correct answer from the options given below.

Given below are two statements, one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) :

The sum of $n$ terms of the Progression

$1+\frac{1}{2}+\frac{1}{2^{2}}+\frac{1}{2^{3}}+$ is $\frac{2^{n-1}-1}{2^{n-1}}$.

Reason (R) :

Sum of a geometric series having $n$ terms is given by $S_{n}=\frac{a\left(1-r^{n}\right)}{1-r}$, where $a$ is the $1^{\text {st }}$ term and $r$ is the common ratio.