Write an explicit formula for the geometric sequence 2, 10, 50, 250.

1. Divide the second term by the first: 10/2 = 5, so the common ratio is 5. 2. The first term is 2. 3. Substituting into a_n = a_1 r^(n-1) gives a_n = 2 * 5^(n - 1). 4. Testing n = 3 gives 2 times 25 = 50, which matches the third term. 5. Swapping the first term and the ratio gives 5 * 2^(n - 1), which starts at 5 rather than 2. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.3 Geometric Sequences_