Geometric progression + logarithm - practice problems
Number of problems found: 29
- Geometric series
How many terms of the geometric series 8+4+2+1+0.5+... must be taken for the sum to get within 10 to the power minus 4 of its sum to infinity? - Robinson 82579
Robinson Crusoe came to the island with 4 grains of corn. How many years did it take him to grow enough grain for bread if he got 10 grains from one grain on average and he needed at least 1kg of bole for 1 bread, and 1 grain weighs about 0.2g? (assume on - Calculate 81860
The two terms of the geometric sequence are a2=12 and a5=three halves. a) calculate the tenth term of the sequence. b) calculate the sum of the first 8 terms of the sequence. v) how many first terms of the sequence need to be added so that the sum is equa - The terms
The terms 1/64, 1/32, and 1/16 form a geometric progression (GP). If the sum of the GP is (2³6 – 2^-6), find the number of terms.
- Principal 67954
How long in months will the principal raise 5,000 euros at 5% p.. a. interest 350 euros? - MP3 player
Mary plans to buy a new MP3 player for 90 USD. And every month, the amount he saved in the previous month doubles. If she saves 3 USD in the first month, how many months will Mary save enough to buy an MP3 player? - Deposit and saving
How long will the deposit of € 2,000 increase at an interest rate of 4.6% p. a. at 2500 €? (Ideally, calculate without logarithms) - GP sequence
Find the remaining unknown characteristics in the finite geometric sequence, if given: a1 = 5, an = 320, sn = 635, n =? q =? - Finite geometric sequence
Find the remaining unknown characteristics in the finite geometric sequence, if given: a1 = 18, an = 13122, sn = 19674, n =? q =?
- Two geometric progressions
Insert several numbers between numbers 6 and 384 so that they form with the given GP numbers and that the following applies: a) the sum of all numbers is 510 And for another GP to apply: b) the sum of entered numbers is -132 (These are two different geome - Interest 37571
We will deposit € 10,500 at the bank at 1.1% interest, and we want to withdraw € 11,000. How many years do we have to wait? Round to 2 decimal places. - Withdraw 37161
We will put € 8,500 into the bank at 1.3% interest, and we want to withdraw € 8,700. How many years do we have to wait? Round to 2 decimal places. - Diameter 36363
With a single pull, the wire diameter is reduced by 10%. How many draws are required to minimize the wire diameter from 5 mm to less than half? - Growth of wood
The annual growth of wood in the forest is estimated at 2%. In how many years will make the forest volume double?
- Pilsen circus
A city citizen saw the circus's arrival in Pilsen in the morning at 08:00. He passed this information at 08:15 to three other city residents. Each of these three people then informed the other three residents at 08:30, and again at 08:45, they reported th - Microorganisms
The first generation of microorganisms has a population of 13500 members. Each subsequent generation is 11/10 times the previous one. Find out how many generations will reach at least three times members of the first generation. - Geometric progression
In geometric progression, a1 = 7, q = 5. Find the condition for n to sum first n members is sn≤217. - Population 4485
The population is 22000 people. With an annual increase of 1.4%, there will be 25,000 people. How many years will it be? - Precision 3390
The price of the device is reduced by one-fifth every year. How long before the price of the device drops to one-tenth of the price? Specify years and months with precision.
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