System of equations + arithmetic progression - practice problems
Number of problems found: 38
- The sum 39
The sum of the first six terms of the arithmetic sequence is 72, and the second term is seven times the fifth term. Find the first term and the AP difference. - 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. - Arithmetic 81811
In which arithmetic sequence is the sum of the first five terms with odd indices equal to 85 and the sum of the first five terms with even indices equal to 100? - Arithmetic 81808
An increasing arithmetic sequence has an odd number of terms. The middle term is 302. If we remove the 4 largest terms from the sequence, the middle term will be 296. Determine the difference in the sequence. - Arithmetic 80808
The lengths of the sides of a right triangle form the first 3 terms of the arithmetic sequence. The content is 6cm². - The lengths
The lengths of the twelve poles form an Arithmetic Progression (A. P). If the third pole is 3m and the eighth pole is 5 m, find the (i) Length of the first pole (ii) Sum of the length of the poles - Consecutive 69904
The three numbers that make three consecutive members of an arithmetic sequence have a sum of 60 and a product of 7500. Find these numbers. - The sum 20
The sum of the first six terms of an arithmetic progression is 552, and the sum of the first two terms of the same is 200. Determine the sum of the first 15 terms. - Quantities 60183
Determine the remaining quantities in the finite geometric sequence, given: n = 4, an = 12.5, sn = 187.5, a1 = ?, q =? - Find two 2
Find two decimals between 4.56 and 6.927 so that the difference between any two consecutive decimals is the same. - Arithmetic 44181
Determine the arithmetic sequence. a3 + a4 = 10 a2 + a5 = 11 - Harry
Harry Thomson bought a large land in the shape of a rectangle with a circumference of 90 meters. He divided it into three rectangular plots. The shorter side has all three plots of equal length. Their longer sides are three consecutive natural numbers. Fi - The sides
The sides of a right triangle form an arithmetic sequence. The hypotenuse is 24 cm long. Determine the remaining sides of the triangle. - 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. - Find d 2
Find d in an A. P. whose 5th term is 18 and 39th term is 120. - The ages
The ages of the four sons make an arithmetic sequence, the sum of which is the father's age today. In three years, the father's age will be the sum of the ages of the three eldest sons, and in the next two and three months, the father's age will be the su - Substitution 19793
Calculate in arithmetic sequence a1, d, s7, if: a1 + a4 + a6 = 71 a5 - a3 - a2 = 2 Hint: Use the substitution method when solving the system. Pay due attention to the "minus" signs in the second equation of the system. - Difference 7873
Find the first term and the difference of the sequence for which it holds: a1 + a6 = 39; a10 - a4 = 18 - Rectangular triangle
The lengths of the rectangular triangle sides with a longer leg of 12 cm form an arithmetic sequence. What is the area of the triangle? - AP RT triangle
The length of the sides of a right triangle forms an arithmetic progression, and the longer leg is 24 cm long. What are the perimeter and area?
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