Question

An arrangement of billiard balls has 5 balls in the first row and 16 rows in all. In each successive row one ball is added. What is the explicit rule for this situation, and how many balls will be in the 16throw?

Answer 1

In the billiard balls arrangement, the explicit rule for the number of balls in the nth row is an = 5 + (n - 1), and there will be 20 balls in the 16th row.

Step-by-step explanation:

The arrangement of billiard balls creates an arithmetic sequence, where the number of balls in a given row can be represented by an explicit rule: an = a1 + (n - 1)d, where a1 is the first term, d is the common difference, and n is the term number. In this case, the first row has 5 balls, and each successive row adds one more ball, so a1 is 5, and d is 1.

To find the number of balls in the 16th row, we apply the rule with n = 16: a16 = 5 + (16 - 1)×1 = 5 + 15 = 20 balls. Thus, there will be 20 balls in the 16th row.