Final answer:
The explicit rule for the sequence of Yuri's monthly incomes is an = $500 × 1.5^(n-1), which represents a geometric sequence where each month's income is 1.5 times the previous month's income.
Step-by-step explanation:
The monthly incomes for the first five months of Yuri's tutoring business are in a geometric sequence with each term increasing by a factor of 1.5 from the previous month. To write an explicit rule for this sequence, we can use the formula for a geometric sequence, which is an = a1 × r(n-1), where an is the n-th term of the sequence, a1 is the first term, r is the common ratio, and n is the term number. In this case, the first term a1 is $500 and the common ratio r is 1.5. Therefore, Yuri's income for the n-th month can be expressed as an = $500 × 1.5(n-1).