Question

Heavy rain in Mark's town caused the river to rise. The river rose three inches the first day, and each day tripled as much as the previous day. What was the river's height on the fourth day?

a) 9 inches
b) 12 inches
c) 15 inches
d) 18 inches

Answer 1

Calculating the geometric progression, the river's height on the fourth day would be 81 inches, which is not one of the provided options.

Step-by-step explanation:

The question describes a geometric progression where the river's height rises by a certain factor each day. The river rose three inches on the first day, and then tripled each subsequent day. To find the height on the fourth day, we can use the formula for the nth term of a geometric sequence, which is a_n = a_1 × r^{(n-1)}, where a_1 is the first term, r is the common ratio, and n is the term number.

• First day: 3 inches
• Second day: 3 inches × 3 = 9 inches
• Third day: 9 inches × 3 = 27 inches
• Fourth day: 27 inches × 3 = 81 inches

Therefore, the river's height on the fourth day would be 81 inches, which is not one of the options given (a) 9 inches (b) 12 inches (c) 15 inches (d) 18 inches.