一组歌手排成5排。第二排有7名歌手。每一排都比它前面的一排多 $n$ 名歌手。

1. Express the number of singers in the first row in terms of $n$

Since each row has $n$ more singers than the row in front of it, the first row has $n$ fewer singers than the second row.
Number of singers in the first row = $7 - n$

1. Express the number of singers in the fourth row in terms of $n$

Since the second row has $7$ singers, the third row has $7 + n$ singers, and the fourth row has $7 + 2n$ singers.

2. Form an equation and solve for $n$

$7 + 2n = 13$
$2n = 13 - 7$
$2n = 6$
$n = 3$

1. Determine the number of singers in each of the 5 rows

From parts (a) and (b), the first row has $4$ singers and the common difference is $n = 3$.
The number of singers in the 5 rows are: $4, 7, 10, 13, 16$.

2. Calculate the total number of singers

$\text{Total} = 4 + 7 + 10 + 13 + 16 = 50$