Question

The front row of an auditorium has $28$ seats. Each of the remaining row has $3$ more seats than the row in front of it. Find the number of seats in the auditorium if there are $32$ rows in it.

• A. $1,440$
• B. $2,384$
• C. $2,688$
• D. $2,784$
• E. $3,552$

Answer 1

Answer: (B)

$2,384$

Given that front row of an auditorium has $28$ seats .

And each remaining row has $3$ more seats then the row in front of it

Then seat arrangement as $28,31,\mathrm{34......}$

Then this is arithmetic procession who first term is $28$ and common difference is $3$.

Then total seats in auditorium up to $32$ row $S=$ $\frac{n}{2}[2a+(n-1\left)d\right]$

$=\frac{32}{2}[2\times 32+(32-1\left)3\right]$

$=16(56+93)$

$=16\times 149$

$=2384$