Question

Cris' cafe is increasing its customer base by advertising. On the first day of the campaign, they had 3 customers. On the second day, they had 11, and on the third day, they had 19. If the increase in customers continues in the same pattern, what is the recursive formula that models the arithmetic sequence?

Answer 1

The recursive formula for the arithmetic sequence representing the increase in customers is an = an-1 + 8, with a starting value of a1 = 3.

Step-by-step explanation:

The question is seeking a recursive formula for an arithmetic sequence, based on the given customer counts for consecutive days. In this arithmetic sequence, the first term is 3, and each successive term increases by the same common difference, which we need to find.

To find the common difference, subtract the first term from the second term (11 - 3 = 8), then subtract the second term from the third term (19 - 11 = 8). Since the common difference is constant and equal to 8, we know that each day 8 more customers are coming compared to the previous day.

The recursive formula for the given arithmetic sequence will then be represented as: an = an-1 + 8, where a1 = 3. This formula states that to find the number of customers on any given day, you take the number of customers from the previous day and add 8.