Geometric Sequences Worksheets Grade 12

1. Emma is a microbiologist studying the growth of a bacterial colony in a laboratory. She observes that the colony follows a geometric growth pattern. Initially, there are 7 bacterial cells. Every 4 hours, the number of cells triples. Emma wants to determine the number of bacterial cells present after 24 hours (the 7th term of the sequence) and the total number of cells that have existed over the entire 24-hour period (sum of the first 7 terms). Find the number of cells at 24 hours and the total number of cells over the first 7 time intervals.
2. Aroha is an environmental scientist monitoring the population of a rare bird species in a protected wetland. She observes that the population follows a geometric growth pattern due to successful conservation efforts. In the first year of her study, there are 9 birds. Each subsequent year, the population increases by a factor of 4 times the previous year's population. Aroha wants to predict the bird population after 10 years (the 10th term of the sequence) and the total number of birds that have lived in the wetland over the first 10 years. Find the population in the 10th year and the total population over the first 10 years.
3. Emma is a botanist studying the population growth of a rare fern species in a protected reserve. She notices that the number of ferns in a specific plot follows a geometric pattern. In the first year, there are 7 ferns. Each subsequent year, the number of ferns triples compared to the previous year. Emma needs to report the number of ferns after 9 years (the 9th term of the sequence) and the total number of ferns that have appeared over the first 9 years. Find the number of ferns in the 9th year and the total number of ferns over the first 9 years.

…and 2 more problems

1. A geometric sequence has its first three terms represented by the areas of three concentric circles. The smallest circle has radius 2 cm, and each subsequent circle's radius increases by a constant factor. If the sum of the areas of the first three circles is 84π cm², what is the common ratio of the geometric sequence formed by the areas?
2. ∑(n=1 to 5) 5 × (-4)^(n-1) = ?
3. Tane is a forestry engineer monitoring the growth of a rare tree species in a conservation plot. He records that the height of a particular tree follows a geometric progression. The tree was 7 cm tall when first measured. Each subsequent year, its height increases by a factor of 3 times the previous year's growth increment (not the total height). In the first year, it grew 7 cm; in the second year, it grew 21 cm; in the third year, it grew 63 cm, and so on. Tane needs to report the total height of the tree after 9 years (the sum of all growth increments from year 1 to year 9) and the height it reached at the end of the 9th year (the 9th term of the sequence of growth increments). Find the growth increment in the 9th year and the total height of the tree after 9 years.

…and 1 more problems

1. ∑(n=1 to 6) 8 × (-2)^(n-1) = ?
2. ∑(n=1 to 6) 5 × (-2)^(n-1) = ?
3. Mason is a materials engineer analyzing the growth of a bacterial biofilm on a metallic surface. He observes that the biofilm area doubles every day. On the first day of measurement, the biofilm covers 7 square millimeters. If this geometric growth pattern continues, what is the total area covered by the biofilm over the first 7 days (including day 1)?

…and 3 more problems