1. **Problem Statement:** We have a marching band forming rows with band members increasing by 2 each row, starting with 7 in the first row. We want to find a general formula for the number of band members in the $n^{th}$ row, find the number in the 9th row, and determine the number of rows if the last row has 25 members. 2. **General Formula:** This is an arithmetic sequence where the first term $a_1=7$ and the common difference $d=2$. The formula for the $n^{th}$ term of an arithmetic sequence is: $$a_n = a_1 + (n-1)d$$ 3. **Apply the formula:** $$a_n = 7 + (n-1) \times 2 = 7 + 2n - 2 = 2n + 5$$ So, the general formula is: $$a_n = 2n + 5$$ 4. **Find $a_9$:** Substitute $n=9$ into the formula: $$a_9 = 2 \times 9 + 5 = 18 + 5 = 23$$ So, there are 23 band members in the 9th row. 5. **Find number of rows if last row has 25 members:** Set $a_n = 25$ and solve for $n$: $$25 = 2n + 5$$ $$25 - 5 = 2n$$ $$20 = 2n$$ $$n = \frac{20}{2} = 10$$ So, there are 10 rows in total. **Final answers:** - General formula: $a_n = 2n + 5$ - $a_9 = 23$ band members - Number of rows if last row has 25 members: 10 rows