Arithmetic Sequences Worksheets Grade 12

1. During a training program, Ava runs 293 meters on the first day and increases the distance by a constant amount each day. On day 15, Ava runs 1077 meters. What is the daily increase in distance?
2. Liam is analyzing the growth of a bacterial culture in a laboratory experiment. The population P(t) (in thousands) after t hours is modeled by the function P(t) = 5e^(0.2t). At what instantaneous rate is the population growing when t = 10 hours? Express your answer in thousands of bacteria per hour.
3. Arithmetic sequence: a₁=14, d=9. Write explicit formula aₙ = ?

…and 6 more problems

1. A pharmaceutical company is modeling the concentration of a new drug in a patient's bloodstream over time. The concentration C(t) in milligrams per liter follows the function C(t) = 50te^(-0.2t), where t is time in hours after administration. The company needs to determine the maximum concentration reached and the time at which it occurs. Find both the time of maximum concentration and the maximum concentration value.
2. Emma's arithmetic sequence: a₁ = 15, d = -5. Write the explicit formula aₙ = ?
3. During a training program, Alex runs 287 meters on the first day and increases the distance by a constant amount each day. On day 15, Alex runs 4949 meters. What is the daily increase in distance?

…and 5 more problems

1. Arithmetic sequence: a₁=7, d=9. Write explicit formula aₙ = ?
2. Arithmetic sequence: a₁=8, d=5. Write explicit formula aₙ = ?
3. A geometric pattern is formed by arranging equilateral triangles in a sequence. The first triangle has side length 2 cm. Each subsequent triangle has side lengths that are 1.5 times the side length of the previous triangle. If this pattern continues infinitely, what is the total area covered by all the triangles? (Area of an equilateral triangle = (√3/4) × side²)

…and 5 more problems