A machine produces (95) units in the first hour and (15) more units each next hour. What is the production in the (15)th hour?

Correct answer: (305)

This is an arithmetic progression because the production increases by the same number, 15 units, every hour. The first term is \\(a=95\\), the common difference is \\(d=15\\), and the fifteenth hour represents the fifteenth term. The formula is \\(a_n=a+(n-1)d\\). Substituting the values gives \\(a_{15}=95+(15-1)\\times15=95+210=305\\). Thus the machine produces 305 units in the fifteenth hour.

Option B is correct. A common mistake is to multiply 15 by 15 without accounting for the first hour, or to use 15 increases instead of the 14 increases that occur before the fifteenth hour. The sequence begins 95, 110, 125, and continues by adding 15. Since reaching the fifteenth term requires fourteen additions, 305 is the required production.