Find a formula for the nth term of the arithmetic sequence shown in the graph.
-Bruce agrees to go to work for Jim at a rate of 1¢ for the first day, 2¢ for the second day, 4¢ for the third day, 8¢ for the fourth day, and so on. What will Bruce's daily pay be on day 18, and how
Much total wages will he have earned at the end of that day?
A) Pay on day 18 = $2621.44; Total pay through day 18 = $1310.71
B) Pay on day 18 = $1310.72; Total pay through day 18 = $2621.43
C) Pay on day 18 = $1310.72; Total pay through day 18 = $1310.71
D) Pay on day 18 = $2621.44; Total pay through day 18 = $2621.43

Question

Quizplus · Accepted Answer

Bruce's pay follows a geometric sequence with the first term a = 1¢ and common ratio r = 2. The nth term is given by a_n = a * r^(n-1). On day 18, a_18 = 1 * 2^(18-1) = 2^17 = 131072¢ = $1310.72. The total pay is the sum of a geometric series: S_n = a * (r^n - 1) / (r - 1). For n = 18, S_18 = 1 * (2^18 - 1) / (2 - 1) = 2^18 - 1 = 262143¢ = $2621.43.

Find a Formula for the Nth Term of the Arithmetic