Question

An employer provides two payment options for employees.

Option A: Receive $200 the first week. Receive an additional $50 for each of the following weeks.
Option B: Receive $200 the first week. Receive an additional 10% for each of the following weeks.

1. Complete the tables to show how much money would be received for both payment options, each week, for 6
weeks.

Answer 1

Option A

`a_n = a_1 + (n - 1)d \\ a_n = 200 + 50(n - 1) \\ a_2 = 200 + 50(2 - 1) = 250\\ a_3 = 200 + 50(3 - 1) = 300 \: \\ a_4 = 200 + 50(4 - 1) = 350 \\ a_5 = 200 + 50(5 - 1) = 400 \\ a_6 = 200 + 50(6 - 1) = 450`

Option B

`\: \: u_(n ) = 200(1 + 0.1) {}^(n - 1) \\ u_(n ) = 200(1.1) {}^(n - 1) \\`

`u_1 = 200(1.1) {}^(1 - 1) = 200 \\ u_2 = 200(1.1) {}^(2 - 1) = 220 \\ u_3 = 200(1.1) {}^(3 - 1) = 242 \\ u_4 = 200(1.1) {}^(4 - 1) = 266.2 \\ u_5 = 200(1.1) {}^(5 - 1) = 292.82 \\ u_6 = 200(1.1) {}^(6 - 1) = 322.102`