Question

In a auditorium the seats are so arranged that there are 8 seats in the first row,11 seats in the second,14 seats in the third etc. thereby increasing the number of seats by 3 every next row. if there are 50 seats in the last row, how many rows of seats are there in the auditorium? Also find the total number of seats in the auditorium​

Answer 1

$\bold\red{\underline{\underline{Answer:}}}$

Given:

Seats in first row=8

Seats in second row=11

Seats in third row=14

The number of seats increase by 3 every next row.

$\bold\orange{To \ find:}$

1)Number of rows in auditorium.

2)Total number of seats in auditorium.

$\bold\green{\underline{\underline{Solution}}}$

The number of seats is in A.P. as it increases 3 seats next row.

$\bold{Let \ seats \ in \ first \ row \ be \ t1}$

$\bold{Seats \ in \ second \ row \ be \ t3}$

Here,t1=a=8,t2=11,t3=14,d=3,tn=50

1)

$\bold{tn=a+(n-1)d}$

$\bold{50=8+(n-1)×3}$

$\bold{50-8=(n-1)3}$

$\bold{42=(n-1)3}$

$\bold{\frac{42}{3}=n-1}$

$\bold{n=14+1}$

$\bold{n=15}$

Therefore in 15th row there are 50 seats.

2)

$\bold{Sn=\frac{n}{2}[t1+tn]}$

$\bold{S15=\frac{15}{2}[8+50]}$

$\bold{S15=\frac{15}{2}×58}$

$\bold{S15=15×29}$

$\bold{S15=435}$

Therefore there are 435 seats in auditorium.

$\bold\red{There \ are \ 15 \ rows \ and \ 435 \ seats \ in }$

$\bold\red{auditorium.}$