A machine produces (140) units in the first hour and (22) more units each next hour. What is the production in the (14)th hour?

Correct answer: (426)

The production figures form an arithmetic progression. The first-hour production is the first term, \\(a=140\\), and the increase each hour is the common difference, \\(d=22\\). The 14th hour is the 14th term, so use \\(a_n=a+(n-1)d\\). Thus \\(a_{14}=140+(14-1)22=140+286=426\\) units.

Option C is therefore correct. There are 13 increases from the first hour to the fourteenth hour, because the first hour already starts at 140 units. Adding 22 fourteen times would incorrectly count one extra increase and produce 448. The sequence begins 140, 162, 184, and continues by adding 22 each time, which confirms the arithmetic. The supplied answer is correct and the instruction to treat the hour number as the term number is appropriate.