Geometric Sequences Worksheets Grade 12

1. Is 4, 12, 36, 108... geometric? Find common ratio
2. Sophia is an architect designing a modern art installation. The structure consists of a series of triangular panels arranged in a vertical tower. The area of the first panel is 192 square centimeters. Each subsequent panel's area is 3/4 of the area of the panel directly below it. If the pattern continues indefinitely, what is the total area of all the panels in the infinite tower?
3. Charlotte is a microbiologist studying the growth of a bacterial colony in a petri dish. She observes that the colony's area increases by a factor of 1.25 every day. On the first day, the area is 16 cm². She wants to predict the area on the nth day. Identify the type of sequence, find the common ratio, and write the explicit formula for the area Aₙ in cm² on day n.

…and 4 more problems

1. Matiu is a biologist studying the spread of a fungal infection in a native forest. He observes that the area covered by the fungus doubles every 12 days. Initially, the fungus covers 15 square meters. Matiu wants to predict the area covered after 60 days using a geometric sequence model. Write the explicit formula for the area covered after n days, where n is a multiple of 12, and then use it to find the area after 60 days.
2. Is 12, 36, 108, 324... geometric? Find common ratio
3. Matiu is studying a chain of interconnected pendulums in his physics class. The length of the first pendulum is 160 cm. Each subsequent pendulum in the chain has a length that is 85% of the length of the previous pendulum. If the pattern continues indefinitely, what is the total length of all the pendulums in the infinite chain?

…and 4 more problems

1. Is 15, 45, 135, 405... geometric? Find common ratio
2. Hana is training for a marathon by following a recovery plan that reduces her weekly running distance by a constant percentage each week. In the first week, she runs 40 km. In the second week, she runs 32 km. In the third week, she runs 25.6 km. Determine the common ratio of this geometric sequence and write an explicit formula for the distance she runs in week n.
3. Is 5, 15, 45, 135... geometric? Find the common ratio r = ?

…and 3 more problems