Question

In an arithmetic progression, the $24th$ term is $100$. Then, the sum of the first $47$ terms of the arithmetic progression is

• A. $2300$
• B. $2350$
• C. $2400$
• D. $4700$

Answer 1

The correct option is D

$4700$

Explanation for the correct option:

Finding the sum of first $47$ terms:

As per the given information,

$\begin{array}{rcl}a+\left(24-1\right)d& =& 100\left[BynthtermofAP=a+\left(n-1\right)d\right]\\ \Rightarrow a+23d& =& 100...\left(1\right)\end{array}$

Sum of $n$ terms of AP, $S_n=\frac{n}{2}\left[2a+\left(n-1\right)d\right]$

So,

$\begin{array}{rcl}{S}_{47}& =& \frac{47}{2}\left[2a+\left(47-1\right)d\right]\\ & =& \frac{47}{2}\left[2a+46d\right]\\ & =& 47\left[a+23d\right]\\ & =& 4700\left[\mathrm{from}\left(1\right)\right]\end{array}$

Hence, option D is correct.