Question

Maya saves $2 after cashing her paycheck. She challenges herself to save $1 more each week than the previous week. The sequence below shows the amounts Maya wants to save each week for the first 5 weeks. Which recursive formula can be used to determine the number of dollars, a (n), Maya saves during the nth week? a (2) = 1 a (n) = a (n-1) +1 2, 3, 4, 5, 6 a (1) = 2 a (n)= a(n-1) +1 a (1) = 2 a (n) = a (n-1) + 2 a (1) = 1 a (n) = a (n-1) +2​

Answer 1

The recursive formula that can be used to determine the amount Maya saves during the nth week is a(1) = 2 and a(n) = a(n-1) + 1, reflecting an arithmetic sequence with a common difference of one dollar.

Step-by-step explanation:

The student wants to know which recursive formula can be used to determine the dollars Maya saves during the nth week. Looking at the sequence provided (2, 3, 4, 5, 6), we can see it's an arithmetic sequence where each term is one dollar more than the previous term. This gives us the recursive formula:

• a(1) = 2
• a(n) = a(n-1) + 1, for n > 1

This formula denotes that the first term, a(1), is $2 and each subsequent term is the previous term plus one dollar. Thus, the correct option is a(1) = 2 and a(n) = a(n-1) + 1.