Equation + geometric progression - practice problems - page 2 of 4
Number of problems found: 78
- The sum 21
The sum of a geometric progression's 2nd and 3rd terms is six times the 4th term. Find the two possible values of the common ratio B. If the second term is eight, the common ratio is positive. Find the first six terms. - GP sequence
Find the remaining unknown characteristics in the finite geometric sequence, if given: a1 = 5, an = 320, sn = 635, n =? q =? - Quantities 60183
Determine the remaining quantities in the finite geometric sequence, given: n = 4, an = 12.5, sn = 187.5, a1 = ?, q =? - Finite geometric sequence
Find the remaining unknown characteristics in the finite geometric sequence, if given: a1 = 18, an = 13122, sn = 19674, n =? q =?
- Members
A geometric sequence with six members has the sum of all six members equal to 63; the sum of the even members (that has an even index) has a value of 42. Find these members. - Insert
Insert five numbers between 8 and 27 such numbers that, with two given ones, they form the first seven members of the geometric sequence. - Straight-line depreciation
Olsen Inc. Purchased a $580,000 machine to manufacture a specialty tap for electrical equipment. The tap is in high demand, and Olsen can sell all it can manufacture for the next ten years. To encourage capital investments, the government exempts taxes on - 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 - Consecutive 46781
We get three consecutive GP members if we subtract the same number from 33, 45, and 63. Determine this GP and calculate its fifth member.
- Equation 46771
Insert three numbers between the roots of the equation 4x² - 17x + 4 = 0 so that they form with the given GP numbers - The block
The block, the edges formed by three consecutive GP members, has a surface area of 112 cm². The sum of the edges that pass through one vertex is 14 cm. Calculate the volume of this block. - Sequences AP + GP
The three numbers that make up the arithmetic sequence have the sum of 30. If we subtract from the first 5, the second 4, and keep the third, we get the geometric series. Find AP and GP members. - 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. - Population 37561
The population increased from 29,000 to 31,500 in 5 years. Calculate the average annual population growth in%.
- Annual growth
The population has grown from 25,000 to 33,600 in 10 years. Calculate what the average annual population growth in% was. - 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? - Consecutive members
The block has a volume of 1728 cm³. Determine the lengths of the edges a, b, and c of the blocks for which a < b < c and a + b + c = 38 cm and whose numerical values in cm represent three consecutive members of the geometric sequence. - Beginning 34991
At the beginning of the year, the company had CZK 5,000,000 in its account. He has the money saved at a 16% interest rate. How much was the interest for the first year? How much was the interest for the second year?
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