Question 1039326
An auditorium has 20 seats on the first row, 24 seats on the second row, 28 seats on the third row, and so on and has 30 rows of seats. How many seats are in the theatre?
<pre>This scenario represents an arithmetic progression (AP), and the formula for the sum of an AP is used: {{{S[n] = (n/2)(2a[1] + (n - 1)d)}}}, with:
n, or number in series: 30; {{{a[1]}}}, or 1st term: 20, and d, or common difference = 4 
{{{S[30] = (30/2)(2(20) + (30 - 1)4)}}}
{{{S[30] = 15(40 + 4(29))}}}
{{{S[30] = 15(40 + 116)}}}
{{{S[30] = 15(156)}}}
{{{highlight_green(matrix(1,7, S[30], or, number, of, seats, "=", "2,340"))}}}