1. **State the problem:** We are given a sequence with terms $a_1=7$, $a_2=35$, $a_3=175$, and $a_4=875$. We need to find a function $a_n$ that represents this sequence. 2. **Identify the pattern:** Notice that each term seems to be multiplied by 5 to get the next term: $$\frac{a_2}{a_1} = \frac{35}{7} = 5, \quad \frac{a_3}{a_2} = \frac{175}{35} = 5, \quad \frac{a_4}{a_3} = \frac{875}{175} = 5.$$ This means the sequence is geometric with common ratio $r=5$. 3. **General formula for geometric sequences:** $$a_n = a_1 \times r^{n-1}$$ where $a_1$ is the first term and $r$ is the common ratio. 4. **Substitute values:** $$a_n = 7 \times 5^{n-1}$$ 5. **Final answer:** The function representing the sequence is $$a_n = 7 \times 5^{n-1}.$$