In the known arithmetic sequence {an}, A1 = 1, a7 = 4, the sequence {BN} is an arithmetic sequence, B1 = 6, B2 = A3 Satisfy a26bn a26 X bn

In the known arithmetic sequence {an}, A1 = 1, a7 = 4, the sequence {BN} is an arithmetic sequence, B1 = 6, B2 = A3 Satisfy a26bn a26 X bn

A7 = a1 + 6D, d = 1 / 2, an = 1 + (n-1) 1 / 2
a26=1+25/2=13.5 a3=2
q=b2/b1=2/6=1/3
bn=b1*q^(n-1)=6/[3^(n-1)]
When 13.5bn ＜ 1, n-1 ＞ 4, n ＞ 5
The smallest integer of n is 6
The tolerance of sequence an is (4-1) / (7-1) = 0.5
a3=1+2×0.5=2
The common ratio of sequence BN is 2 △ 6 = 1 / 3
bn=6×(1/3)^(n-1)
a2=1+0.5=1.5
1.5*6*(1/3)^(n-1)3
The minimum integer n is 4
It is known that {an} is an arithmetic sequence, {BN} is an equal ratio sequence, and A1 = B1 = 2, B4 = 54, a1 + A2 + a3 = B2 + B3. (1) find the general term formula of {an} and {BN}; (2) find the first n term and Sn of {CN} if {CN} satisfies CN = anbn
(1) Let the tolerance of {an} be D, and the common ratio of {BN} be Q. from B4 = b1q3 = 54, Q3 = 542 = 27, thus q = 3, so BN = B1 & nbsp; · & nbsp; QN − 1 = 2 & nbsp; · & nbsp; 3N − 1 (3 points) and a1 + A2 + a3 = 3a2 = B2 + B3 = 6 + 18 = 24, A2 = 8, thus d = a2-a1 = 6, so an = a1 + (n-1) · 6 =
It is known that an is an arithmetic sequence, BN is an arithmetic sequence, and A1 = B2 = 2, B4 = 54, a1 + A2 + a3 = B2 + B3
1. Find the general term formula of sequence BN 2. Find the first ten terms and S10 of sequence an
Because BN is equal ratio, and because B2 = 2, B3 = A2 + a3, B4 = 54, Q square = 27, then q = plus or minus 3 times the root sign 3, and then B1 = 2 times the root sign 3 divided by 9, BN general term comes out, which is the N-1 times of BN = A1 times q... it's too boring to bring it in. After 2 B3 comes out, you can use B3 = A2 + a3
bn=2.3√3^n/27
an=(2√3-4/3)n+10/3-2√3
S10=90√3-40
b2=2，b4=54
The common ratio can be obtained;
The general term BN can be written
a1+a2+a3=b2+b3
A1 + A1 + D + A1 + 2D = B2 + B3
Because A1 knows, D can be found
So an can calculate the first 10 terms and
Mathematical rule of removing brackets and simplification of absolute value
a＋(b－c﹚＝a＋b－c a＋﹙b＋c﹚=a＋b＋c
a－(b＋c﹚＝a－b－c a－﹙b－c﹚＝a－b＋c
a±﹙b×c﹚＝a×c±b×c
｜a—b｜=a―b（a＞b） ｜a―b｜=b―a（a＜b）
Taking the three sides of the right triangle ABC as the sides, three equilateral triangles are made outwards with the area of S1, S2 and S3. The relationship between S1, S2 and S3 is determined and proved
Let three times be ABC, corresponding to S1, S2, S3, S1 = the root of four times the square of A. similarly, S2, S3 can be obtained, so S1: S2: S3 = the square of a: the square of B: the square of C, please adopt 3Q
There are three courses: Chinese, mathematics and English. The full score of each course is 100
If the average score of Chinese and English is 94, how much is the average score of Xiaohua
not always.
Chinese + mathematics = 188
English + mathematics = 188
So, Chinese = English
The total score of the three courses is: Chinese + mathematics + English = 188 + English
Therefore, when the English score is the highest, the average score of the three subjects is the highest, and the maximum is (188 + 100) △ 3 = 96 (points)
On the other hand, Chinese + mathematics + English = 188 × 2-mathematics = 376-mathematics
Therefore, when the mathematics score is the highest, the average score of the three gates is the lowest, and the minimum is (376-100) △ 3 = 92 (points)
20 oral problems of decimal multiplication in Grade 5
（1）3.8 × 6.3 =
（2）9.4 × 9.8 =
（3）7.9 × 1.2 =
（4）3.9 × 9.4 =
（5）5.9 × 5.5 =
（6）1.5 × 9.5 =
（7）0.9 × 1.4 =
（8）9.6 × 1.7 =
（9）3.3 × 8.2 =
（10）3.8 × 0.1 =
（11）4.9 × 7 =
（12）7.6 × 3.6 =
（13）4.8 × 8.6 =
（14）7.5 × 7.2 =
（15）6 × 9.6 =
（16）3.5×5=
（17）2.4×0.3=
（18）1.25×0.8=
（19）7.5×0.2=
（20）4.8×1.6=
3(2x+1)(2x-1)-4[(3)/(2)x-3][(3)/(2)+3]
5(2x+5)2+(3x-4)(-3x-4)
(2x+y-z+5)(2x-y+z+5)
[(7)/(3)x+(3)/(2)y]2
3 (2x + 1) (2x-1) - 4 [(3) / (2) x-3] [(3) / (2) + 3] = 3 (4x ^ 2-1) - 4 (9 / 4x ^ 2-9) = 12x ^ 2-3-9x ^ 2 + 36 = 3x ^ 2 + 335 (2x + 5) 2 + (3x-4) (- 3x-4) = 20x + 50-9x ^ 2 + 16 = 9x ^ 2 + 20x + 66 (2x + Y-Z + 5) (2x-y + Z + 5) as above, pay attention to the application of square difference formula
As shown in figure (2), take the three sides of the right triangle ABC as the sides, and make three equilateral triangles outward, with the areas of S1, S2 and S3 respectively
S1 = quarter root sign 3 * a ^ 2 / 4 how can you explain this step
S1 corresponding to the triangle side length is a, let the height be h, the upper, lower half and one side form an equilateral triangle, H ^ 2 = a ^ 2 - (A / 2) ^ 2, the solution is h = two-thirds root sign three, and then the area is equal to (root sign three * a ^ 2) / 4, you have four more
Elementary school fourth grade Mathematical Olympiad 50 simple questions and answers
There must be more than 20 answers
1. Colored flags were planted on one side of the road every 5 meters. A total of 10 flags were planted from the beginning to the end. How long is the road?
2. On both sides of the corridor of the school, a pot of chrysanthemum was put every 4 meters. A total of 18 pots were put from the beginning to the end. How long is the corridor?
3. How many balloons can be hung on a 20 meter long rope every 5 meters from one end?
4. Five colored flags were planted on one side of a 32 meter long highway from the beginning to the end. The distance between two adjacent flags is equal. How many meters is the distance between two adjacent flags?
5. Put chairs on both sides of a 25 meter long road in the park. There are 12 chairs from the beginning to the end. The distance between two adjacent chairs is equal. How many meters is the distance between two adjacent chairs?
6. There is a piece of wood that needs to be sawn into eight sections. It takes two minutes to cut each section. How many minutes does it take to finish all the sawing?
7. A piece of wood needs to be sawn into four sections. It takes five minutes to cut each part. How many minutes does it take to finish the whole sawing?
8. It took 15 minutes to saw a log into a 2-meter-long section. It takes 3 minutes to saw each section. How long is the log?
9. When Xiao Ming climbs the stairs, he has to walk 12 steps on each floor, and it takes 2 seconds to walk one step. How long does it take Xiao Ming to walk from the first floor to the fourth floor?
10. Around a rectangular garden with a circumference of 42 meters, how many potted flowers can be put every 2 meters?
11. We need to plant trees around a pool. It is known that the perimeter of the pool is 245 meters. We plan to plant 49 trees. The distance between two adjacent trees is equal. How many meters is the distance between two adjacent trees?
12. Surround a fence around a square with a side length of 12 meters, and drive a wooden pile every 4 meters. How many wooden piles should be prepared in total?
13. Children plant trees, first plant one tree, then plant one tree every three meters, has planted nine. How many meters is the distance between the first tree and the ninth tree?
14. We put colored flags on one side of the road every 5 meters. There are 10 flags from the beginning to the end. How long is the road?
15. In the school corridor on both sides, every 4 meters put a pot of chrysanthemum, from the beginning to the end of a total of 18 pots, how many meters of this corridor?
16. Hang balloons on a 20 meter long rope. From one end, hang balloons every 5 meters. How many balloons are there?
17. A and B compete to climb the stairs. A runs to the fifth floor and B just runs to the third floor. According to this calculation, a runs to the 17th floor and B runs to how many floors?
18. Xiaoming and Xiaohong climb the stairs to compete. Xiaoming runs to the 4th floor, and Xiaohong just runs to the 5th floor. According to this calculation, Xiaoming runs to the 16th floor, and Xiaohong runs to the 4th floor?
19. Two students compete to climb stairs. No. 1 climbs to the sixth floor and No. 2 climbs to the ninth floor. When No. 1 climbs to the eleventh floor, which floor should No. 2 climb to?
20. A climbs twice as fast as B. when B climbs to the sixth floor, what floor does a climb to?
21. It took 28 minutes to saw a steel pipe into small sections. It is known that it takes 4 minutes to saw each section. How many sections has the steel pipe been sawed into?
22. There is a piece of wood that needs to be sawn into four sections. It takes five minutes to cut each section. How many minutes does it take to finish the whole sawing?
23. It took 15 minutes to saw a log into a 2-meter-long section. It takes 3 minutes to saw each section. How long is the log?
24. When Xiao Ming climbs the stairs, he has to walk 12 steps on each floor. It takes 2 seconds to walk one step. How long does it take Xiao Ming to walk from the first floor to the fourth floor?
25. There is a 180 cm long rope. Starting from one end, mark every 3 cm and every 4 cm. Then cut off the marked place. How many pieces of the rope have been cut?
26. On a long wooden stick, there are three kinds of scale marks. The first scale marks divide the stick into ten equal parts, the second scale marks divide the stick into twelve equal parts, and the third scale marks divide the stick into fifteen equal parts. If the stick is sawed along each scale mark, how many sections will the stick be sawed into?
27. One day after the heavy snow, Xiao Ming and his father walked together to measure the perimeter of a circular flower bed. Their starting point and direction were exactly the same. Xiao Ming's average step length was 54 cm, and his father's average step length was 72 cm. Because their footprints overlapped, and they all returned to the starting point after a walk, only 60 footprints were left on the snow. What's the perimeter of this flower bed?
28. There is a high-rise building. It takes 2 minutes to go up one floor and 1 minute and 30 seconds to go down one floor. Wang Jun started to walk up from the bottom floor at 12:20, went down immediately after reaching the top floor (no stopover), and returned to the bottom floor at 13:02. How many floors are there in this high-rise building?
29. Starting from 10.15 km away from the forest park, plant trees along the road, and plant one cypress every 50 meters. A car can only pull four trees from the forest park to each planting point at a time. After 12 trees are transported, the car returns to the forest park and asks how much fuel the car consumes at least? (2 kg per 10 km)
The students of grade 30 and grade 5 planted 9 trees into 8 rows on average, each row has 3 trees. Please draw a picture to show how they planted them
31. Xiaoyan found an interesting figure in the guessing room of the children's palace. Nine green lights are arranged in ten rows. Each row has three lights. Please draw its arrangement
How long is the distance between the two adjacent trees? How long is the distance between the two adjacent trees 40 meters?
33. Five colored flags were planted on one side of a 32 meter long highway from the beginning to the end. It is known that the distance between two adjacent colored flags is equal. How many meters is the distance between two adjacent colored flags?
34. Put chairs on both sides of a 25 meter long path in the park, and put 12 chairs equidistant from the start to the end. How many meters is the distance between two adjacent chairs?
35. A piece of wood needs to be sawn into 8 sections. It takes 2 minutes to cut each section. How many minutes does it take to finish the whole sawing?
35. There are 20 poles at both ends of a road every 5 meters. How long is the road?
37. On both sides of a 30 meter long corridor, put a pot of flowers every 5 meters. How many pots of flowers do you need to put in this way?
38. A lake is 1800 meters long. A willow tree is planted every 3 meters around the lake. A peach tree is planted between two willows. How many willows and peaches are planted around the lake?
39. There are three pieces of wood. I plan to saw each piece into three sections. It will take three minutes to cut one place. How long does it take to finish all the sawing?
40. There is a wall clock, which rings every hour. What time does it ring? How many times does it ring? How many seconds does it finish?
41. There is a 17 storey house with 17 steps between two adjacent floors. How many steps does a person have to climb from the first floor to the eleventh floor?
42. Someone goes to the eighth floor of a ten story building to do business. Unfortunately, there is a power failure and the elevator stops. If it takes 48 seconds to walk from the first floor to the fourth floor, how long will it take to go up to the eighth floor at the same speed?
43. An old man walked on the road at the same speed. It took 12 minutes to walk from the first pole to the 12th pole. The old man walked at the same speed for 24 minutes. Which pole should he walk to?
44. The scientists carried out an experiment and made records every five hours. When they made the twelfth record, the clock turned the right hand