# Geometric progression + exponentiation - practice problems

#### Number of problems found: 44

- Finite geometric sequence

Find the remaining unknown characteristics in the finite geometric sequence, if given: a1 = 18, an = 13122, sn = 19674, n =?, q =? - Seventh term

The first term of a geometric sequence is 9 and the third term is 1296. Find the seventh term. - Monthly payments 2

Suppose you have selected a new car to purchase for $19,500. If the car can be financed over a period of 4 years at an annual rate of 6.9% compounded monthly, how much will your monthly payments be? - The town

The town population is 56000. It is decreasing by 2% every year. What will be the population of the town after 13 years? - Annual increase

The number of cars produced increased from 45,000 to 47,000 in 3 years. Calculate the average annual increase in cars in%. - What is 10

What is the 5th term, if the 8th term is 80 and common ratio r =1/2? - If the 3

If the 6th term of a GP is 4 and the 10th is 4/81, find common ratio r. - The half life

The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 145 grams of a radioactive isotope, how much will be left after 3 half-lives? - Savings

The depositor regularly wants to invest the same amount of money in the financial institution at the beginning of the year and wants to save 10,000 euros at the end of the tenth year. What amount should he deposit if the annual interest rate for the annua - Five element

The geometric sequence is given by quotient q = 1/2 and the sum of the first six members S_{6}= 63. Find the fifth element a_{5}. - Volume of wood

Every year, at the same time, an increase in the volume of wood in the forest is measured. The increase is regularly p% compared to the previous year. If in 10 years the volume of wood has increased by 10%, what is the number p? - Six speeds

A drilling machine is to have 6 speeds ranging from 50 to 750 revolutions per minute. If the speed forms a geometric progression, determine their values. - Three members GP

The sum of three numbers in GP (geometric progression) is 21 and the sum of their squares is 189. Find the numbers. - Investment 2

Jack invested $5000 in a 5-month term deposit at 4.7% p. A. . At the end of the 5-months, jack reinvested the maturity value from the first deposit into an 11-month term deposit at 7.3% p. A. What is the maturity value at the end of the second term deposi - Curiosity factor

A blogger starts a new website, initially the number of the traffic is 293 due to their curiosity factor. The business owner estimated that the traffic will increase by 2,6% per week. What will be the number of it in week 5?. - The machine

The annual depreciation of the machine is 10%. After 8 years, the machine is worth 697 euros. What was the price of this machine at the time of purchase? - Profit growth

The profit of a company increased by 25% during the year 1992, increased by 40% during the year 1993, decreased by 20% in 1994 and increased by 10% during the year 1995. Find the average growth in the profit level over the four years periods? - Geometric progression

In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is sn≤217. - Radioactive material

A radioactive material loses 10% of its mass each year. What proportion will be left there after n=6 years? - Investment

1000$ is invested at 10% compound interest. What factor is the capital multiplied by each year? How much will be there after n=12 years?

Do you have an exciting math question or word problem that you can't solve? Ask a question or post a math problem, and we can try to solve it.

Geometric progression - practice problems. Exponentiation - practice problems.