Question

A meeting hall has $20$ seats in the first row, $24$ seats in the second row, $28$ seats in the third row, and so on and has in all $30$ rows. How many seats are there in the meeting hall?

• A. $2120$
• B. $2340$
• C. $2540$
• D. $2890$

Answer 1

Answer: (B)

$2340$

Seats are in first row $=20$ , seats are in second row $=24$,seats are in third row $=28$........and so on..
This series becomes an AP with first term $a=20$ and common difference $d=24-20=4$.
To find all the seats in meeting hall with $30$ rows we have to find the sum of this AP up to $30$ terms.
Hence $S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
$\Rightarrow S_{30}=\frac{30}{2}[2\times 20+(30-1\left)4\right]$
$\Rightarrow S_{30}=15[40+29\times 4]$
$\Rightarrow S_{30}=15\left[156\right]$
$\Rightarrow S_{30}=2340$