Geometric Sequences Worksheets Grade 12

1. Isabella is a financial analyst for a renewable energy company. The company's revenue has been growing geometrically due to increased solar panel installations. In the first year of tracking, the revenue was $8,000. Each subsequent year, the revenue multiplies by a factor of 2.5. Isabella needs to present the revenue projections for the 7th year and the total cumulative revenue over the first 7 years to the board of directors. Determine the revenue in the 7th year and the total revenue over the first 7 years.
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. Isabella is constructing a visual pattern using a series of nested regular heptagons. The outermost heptagon has a side length of 42 cm. Each subsequent heptagon is formed by connecting the midpoints of the sides of the previous heptagon, creating a smaller rotated heptagon inside. The side lengths of these heptagons follow a geometric sequence with a common ratio of 0.7. What is the side length of the 7th heptagon, and what is the sum of the perimeters of the first 7 heptagons? (Perimeter of a regular heptagon = 7 × side length)
2. Olivia is a financial analyst studying the growth of a company's quarterly revenue. The revenue in the first quarter was $5000. The company projects that each subsequent quarter, the revenue will be 1.2 times the previous quarter's revenue. Olivia needs to present the projected revenue for the 10th quarter and the total projected revenue over the first 10 quarters to the board. Find the revenue in the 10th quarter and the total revenue over the first 10 quarters.
3. Mere is a materials engineer testing the decay of a rare metal's conductivity under repeated stress cycles. She observes that the conductivity (in Siemens per metre) follows a geometric sequence. The initial conductivity is 64 S/m. After each stress cycle, the conductivity decreases to 3/4 of its previous value. Mere needs to report the conductivity after the 6th cycle (the 6th term) and the total conductivity loss (the sum of the first 6 terms) for a safety analysis. Find the conductivity after the 6th cycle and the sum of the conductivities over the first 6 cycles.

…and 2 more problems

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. Tane is constructing a visual pattern using a series of nested regular pentagons. The largest pentagon has a side length of 45 cm. Each subsequent pentagon is inscribed within the previous one by connecting the midpoints of its sides, forming a smaller rotated pentagon inside. The side lengths of these pentagons follow a geometric sequence. The common ratio for this pattern, derived from the geometry of connecting midpoints of a regular pentagon, is given by the golden ratio conjugate: r = (sqrt(5) - 1)/2. What is the side length of the 7th pentagon, and what is the sum of the perimeters of the first 7 pentagons? (Perimeter of a regular pentagon = 5 × side length)
3. Mere is a marine biologist studying the population growth of a rare species of sea star in a protected marine reserve. She observes that the number of sea stars in a specific quadrat follows a geometric pattern. In the first year of her study, there are 8 sea stars. Each subsequent year, the population increases by a factor of 4 (the number of sea stars quadruples each year). Mere wants to know the population size after 6 years (the 6th term of the sequence) and the total number of sea stars that have been present in the quadrat over the first 6 years. Find the population in the 6th year and the total population over the first 6 years.

…and 3 more problems