Chapter MPS, Problem 11.1MPS

a.

To determine

Number of seats in last row.

Answer to Problem 11.1MPS

There will be $127$ in the last row of the section.

Explanation of Solution

Given information:

A section has 30 rows.

Seats in first row = 11 seats

Seats in second row = 15 seats

Seats in third row = 19 seats

Formula used:

Nth term of arithmetic sequence:

  $a_n=a+\left(n-1\right)d$

  a = First term of the series.

  d = Common difference

  n= Number of terms

  $a_n$ = nth term

As we can see the number of seatsin rows are increasing in Arithmetic progression as their common difference is same:

Seat in row 3 − seat in row 2 = $19-15=4$

Seat in row 2 − seat in row 1 = $15-11=4$

As we can see above the common difference(d) is 4 between two consecutive rows.

Now finding the seats in the last row using formula $a_n=a+\left(n-1\right)d$ .

Here $a=11,d=4,n=30$

  $\begin{array}{l}{a}_{30}=11+\left(30-1\right)4\\ a_{30}=11+\left(29\right)4\\ a_{30}=11+116\\ \boxed{a_{30}=127}\end{array}$

There will be $127$ in the last row of the section.