Question

There are $20$ rows of seats in a conference hall with $20$ seats in the first row, $21$ seats in the second row, $22$ seats in the third row and so on. In total, how many seats are there in the conference hall?

• A. $500$
• B. $550$
• C. $590$
• D. $620$

Answer 1

The correct option is C $590$

Given:-

Total number of rows $\left(n\right)=20$

Seats in first row $\left(a\right)=20$

Seats in second row $\left(a_2\right)=21$

Seats in third row $\left(a_3\right)=22$

Common difference $\left(d\right)=a_3-a_2=22-21=1$

$\Rightarrow \text{Total number of seats in conference hall}\left(S_n\right)=\frac{n}{2}(2a+(n-1)d)$

$\Rightarrow S_{20}=\frac{20}{2}(2\times 20+(20-1)\times 1)$

$\Rightarrow S_{20}=10(40+19)=10\times 59=590$

Hence correct answer is 590.