System of equations + geometric progression - practice problems
Number of problems found: 18
- Difference 81849
Determine four numbers so that the first three form the successive three terms of an arithmetic sequence with difference d=-3 and the last three form the next terms of a geometric sequence with quotient q=one half. - Find k
Find k so that the terms k-3, k+1, and 4k-2 form a geometric sequence. Show your solution. - In a GP 72+144
In a GP, the sum of the 2nd and fifth terms is 72, and the sum of the 3rd and 6th terms is 144. Find the common ratio, find the first term, and find the sum of 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 =? - 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. - 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. - 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. - 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. - GP - three members
The second and third of a geometric progression are 24 and 12(c+1), respectively, given that the sum of the first three terms of progression is 76. determine the value of c. - Calculate 6414
If we add the same number x to the numbers -1,3,15,51, we get the first four members of the geometric sequence. Calculate the number x and the first four members of the geometric sequence. - Geometric 5895
A2 + a3 = -6 a1 + a2 + a3 + a4 = 20 Geometric sequence q, a1? - Geometric seq
Find the third member of geometric progression if a1 + a2 = 36 and a1 + a3 = 90. Calculate its quotient. - Calculate 3339
A1 + a3 = 15 a1 + a2 + a3 = 21 Calculate a1 and q (quotient of the geometric sequence). - Geometric sequence
In the geometric sequence is a4 = 20 a9 = -160. Calculate the first member a1 and quotient q. - Geometric sequence 5
About members of the geometric sequence, we know: 3 a5:a3 = 27:25 7 a3 +5 a7 = 1 : 564 Calculate a1 (first member) and q (common ratio or q-coefficient) - Geometric sequence 3
In geometric sequence is a8 = 312500; a11= 39062500; sn=1953124. Calculate the first item a1, quotient q, and n - number of members by their sum s_n.
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