Question

There are 12 seats in the front row of a theatre

Each row has 2 more seats than the row in front of it

There are 152 seats in total in the theatre
How many rows are there in total

Answer 1

8 rows

Explanation:

We can think of the number of seats in each row as an arithmetic sequence, where the first term, a, = 12 and the common difference, d, = 2. So the sequence would be 12, 14, 16, ... k, and the row corresponds to the position of the term in the sequence. So the sum of n rows (terms) = 152.

Using the formula for sum of terms,

`S_(n) = (n)/(2)(2(12) + 2(n-1)) = 152`

Now we solve for n as follows:

`n(2n+22) = 304 \\\\ 2n^(2) + 22n - 304 = 0 \\\\ n^(2) + 11n - 152 \\\\(n+19)(n-8) = 0 \\\\ n =-19, n = 8`

However we can't have a negative number of rows so we take 8 rows as our solution.