A marching band formation consists of 6 rows. The first row has 9 musicians, the second has 11 , the third has 13 and so on. How many musicians are in the last row and how many musicians are there in all?

To find the number of musicians in the last row and the total number of musicians in the marching band formation, we can observe the pattern in the number of musicians in each row. The number of musicians in each row forms an arithmetic sequence: - Row 1: 9 musicians - Row 2: 11 musicians - Row 3: 13 musicians - Row 4: 15 musicians - Row 5: 17 musicians - Row 6: 19 musicians We can see that the first term \( a_1 = 9 \) and the common difference \( d = 2 \). To find the number of musicians in the last (6th) row, we can use the formula for the \( n \)-th term of an arithmetic sequence: \[ a_n = a_1 + (n - 1) \cdot d \] For the 6th row (\( n = 6 \)): \[ a_6 = 9 + (6 - 1) \cdot 2 = 9 + 5 \cdot 2 = 9 + 10 = 19 \] So, there are 19 musicians in the last row. Next, to find the total number of musicians in all rows, we can use the formula for the sum of the first \( n \) terms of an arithmetic sequence: \[ S_n = \frac{n}{2} \cdot (a_1 + a_n) \] where \( n \) is the number of terms, \( a_1 \) is the first term, and \( a_n \) is the last term. In this case, \( n = 6 \), \( a_1 = 9 \), and \( a_6 = 19 \): \[ S_6 = \frac{6}{2} \cdot (9 + 19) = 3 \cdot 28 = 84 \] Thus, the total number of musicians in all rows is 84. In summary: - The number of musicians in the last row is **19**. - The total number of musicians in all rows is **84**.