It is known that the sum of the first n terms of the arithmetic sequence {an} with tolerance greater than zero is Sn and satisfies a3a4 = 117, A2 + A5 = 22?

It is known that the sum of the first n terms of the arithmetic sequence {an} with tolerance greater than zero is Sn and satisfies a3a4 = 117, A2 + A5 = 22?

In the arithmetic sequence, A2 + A5 = A3 + A4, so
A3a4 = 117, A3 + A4 = 22, and because the tolerance is greater than 0, the solution is A3 = 9, A4 = 13, and tolerance d = 4
So an = A3 + (n-3) * d = 9 + (n-3) * 4 = 4n-3
According to the meaning of the title, (a3-d) + (A3 + 2D) = 22 → d = 22-2a3
Substituting A3 (A3 + D) = 117, A3 (A3 + 22-2a3) = 117 → A3 & # 178; - 22a3 + 117 = 0 → (a3-9) (a3-13) = 0 → A3 = 9 or A3 = 13
It is known that D ＞ 0, A3 = 9, A1 = 1, d = 4
So an = 1 + 4 (n-1) = 4n-3
Because it is an arithmetic sequence, there is A3 + A4 = A2 + A5 = 22;
Because a3a4 = 117;
The results show that: (1) A3 = 9, A4 = 13; (2) A3 = 13, A4 = 9;
The tolerance should be greater than zero, so A3 = 9, A4 = 13;
So the tolerance A1 = 1, d = 4;
So the general formula of the sequence {an} is: an = 4n-3.
Solution: (1) {a n} is an arithmetic sequence
A 3 + a 4 = a 2 + a 5 = 22 and a 3 · a 4 = 117
A 3 and a 4 are two real roots of the equation x 2 - 22x + 117 = 0
The tolerance D ＞ 0, A3 ＜ A4
∴a 3 =9,a 4 =13.
∴ ∴
∴a n =4n-3.
Electric power formula of junior high school physics
Urgent needs
There are four formulas of electric power
1、P = W /t
Unit of physical quantity
P -- electric power W kw
W -- electric work, J kWh
T -- power on time, s h
2、P＝UI：
Unit of physical quantity
P -- electric power W
I-A current
U -- voltage V
3、P=U2/R
4. P = I2R (3,4 can only be used in pure resistance circuit.)
Sixth grade volume 2 oral arithmetic
I want to do 50 mental arithmetic in the second semester of grade 6
With serial number!
1.3/7 × 49/9 - 4/3
2.8/9 × 15/36 + 1/27
3.12× 5/6 – 2/9 ×3
4.8× 5/4 + 1/4
5.6÷ 3/8 – 3/8 ÷6
6.4/7 × 5/9 + 3/7 × 5/9
7.5/2 -（ 3/2 + 4/5 ）
8.7/8 + （ 1/8 + 1/9 ）
9.9 × 5/6 + 5/6
10.3/4 × 8/9 - 1/3
11.7 × 5/49 + 3/14
12.6 ×（ 1/2 + 2/3 ）
13.8 × 4/5 + 8 × 11/5
14.31 × 5/6 – 5/6
15.9/7 - （ 2/7 – 10/21 ）
16.5/9 × 18 – 14 × 2/7
17.4/5 × 25/16 + 2/3 × 3/4
18.14 × 8/7 – 5/6 × 12/15
19.17/32 – 3/4 × 9/24
20.3 × 2/9 + 1/3
21.5/7 × 3/25 + 3/7
22.3/14 ×× 2/3 + 1/6
23.1/5 × 2/3 + 5/6
24.9/22 + 1/11 ÷ 1/2
25.5/3 × 11/5 + 4/3
26.45 × 2/3 + 1/3 × 15
27.7/19 + 12/19 × 5/6
28.1/4 + 3/4 ÷ 2/3
1. 3/7 × 49/9 - 4/3
2. 8/9 × 15/36 + 1/27
3. 12× 5/6 – 2/9 ×3
4. 8× 5/4 + 1/4
5. 6÷ 3/8 – 3/8 ÷6
6. 4/7 × 5/9 + 3/7 × 5/9
7. 5/2 -（ 3/2 + 4/5 ）
8. 7 / 8 + (1 / 8 + 1 / 9
1. 3/7 × 49/9 - 4/3
2. 8/9 × 15/36 + 1/27
3. 12× 5/6 – 2/9 ×3
4. 8× 5/4 + 1/4
5. 6÷ 3/8 – 3/8 ÷6
6. 4/7 × 5/9 + 3/7 × 5/9
7. 5/2 -（ 3/2 + 4/5 ）
8. 7/8 + （ 1/8 + 1/9 ）
9. 9 × 5/6 + 5/6
10. 3/4 × 8/9 - 1/3
11. 7 × 5/49 + 3/14
12. 6 ×（ 1/2 + 2/3 ）
13. 8 × 4/5 + 8 × 11/5
14. 31 × 5/6 – 5/6
15. 9/7 - （ 2/7 – 10/21 ）
16. 5/9 × 18 – 14 × 2/7
17. 4/5 × 25/16 + 2/3 × 3/4
18. 14 × 8/7 – 5/6 × 12/15
19. 17/32 – 3/4 × 9/24
20. 3 × 2/9 + 1/3
21. 5/7 × 3/25 + 3/7
22. 3/14 ×× 2/3 + 1/6
23. 1/5 × 2/3 + 5/6
24. 9/22 + 1/11 ÷ 1/2
25. 5/3 × 11/5 + 4/3
26. 45 × 2/3 + 1/3 × 15
27. 7/19 + 12/19 × 5/6
28. 1/4 + 3/4 ÷ 2/3
29. 8/7 × 21/16 + 1/2
30. 101 × 1/5 – 1/5 × 21
1. Mental arithmetic
(1)58+42= (2)87－45= (3)125×8=
(4)50×12= (5)804÷4= (6)134＋66=
(7)1000－98= (8)720÷5= (9)0÷47=
Equation:
(1)2x+8=16
(2)x/5=10
(3)x+7x=8
(4)9x-3x=6
(5)6x-8=4
(6)5x+x=9
(7)x-8=6x
(8)4/5x=20
(9)2x-6=12
(10)7x+7=14
(11)6x-6=0
(12)5x+6=11
(13)2x-8=10
(14)1/2x-8=4
(15)x-5/6=7
(16)3x+7=28
(17)3x-7=26
(18)9x-x=16
(19)24x+x=50
(20)6/7x-8=4
(30)3x-8=30
(31)6x+6=12
(32)3x-3=1
(33)5x-3x=4
(34)2x+16=19
(35)5x+8=19
(36)14-6x=8
(37)15+6x=27
(38)5-8x=4
(39)7x+8=15
(40)9-2x=1
(41)4+5x=9
(42)10-x=8
(43)8x+9=17
(44)9+6x=14
(45)x+9x=4+7
(46)2x+9=17
(47)8-4x=6
(48)6x-7=12
(49)7x-9=8
(50)x-56=1
(51)8-7x=1
(52)x-30=12
(53)6x-21=21
(54)6x-3=6
(55)9x=18
(56)4x-18=13
(57)5x+9=11
(58)6-2x=11
(59)x+4+8=23
(60)7x-12=8
(61)X-5.7=2.15
(62)15 5X-2X=18
(62)3X 0.7=5
(63)3.5×2= 4.2 x
(64)26×1.5= 2x
(65)0.5×16―16×0.2=4x
(66)9.25－X=0.403
(67)16.9÷X=0. 3
(68)X÷0.5=2.6
(69)x＋13＝33
(70)3 － 5x＝80
(71)1.8- 6x＝54
(72)6.7x －60.3＝6.7
(73)9 ＋4x ＝40
（74）0.2x－0.4＋0.5＝3.7
（75）9.4x－0.4x＝16.2
（76）12 －4x＝20
（77）1/3 x＋5/6 x＝1.4
（78）12 x＋34 x=1
（79）18x－14 x= 12
（80）23 x－5×14 = 14
（81）12 ＋34 x=56
（82）22－14 x= 12
（83）23 x－14 x= 14
（84）x＋14 x= 65
（85）23 x=14 x ＋14
（86）30 x－12 x －14 x=12
Are these OK? Put them away
Q: it is known that the greatest common divisor of two natural numbers is 20 and the least common multiple is 560. What are the two numbers with the least difference among the two numbers that meet the conditions?
Answer: 560 / 20 = 28
28=4*7
The two numbers are
20*4=80
20*7=140
Rule: the product of two numbers is equal to the product of the greatest common multiple and the least common multiple of the two numbers. Q: 1 △ 32 △ 0.05 △ 0.25 △ 0.2
The condition is that you can't use fractions, and you can't extract common terms. A.... Unfold
Q: it is known that the greatest common divisor of two natural numbers is 20 and the least common multiple is 560. What are the two numbers with the least difference among the two numbers that meet the conditions?
Answer: 560 / 20 = 28
28=4*7
The two numbers are
20*4=80
20*7=140
Rule: the product of two numbers is equal to the product of the greatest common multiple and the least common multiple of the two numbers. Q: 1 △ 32 △ 0.05 △ 0.25 △ 0.2
The condition is that you can't use fractions, and you can't extract common terms. A: dividing by several numbers is equal to dividing by their product
Divide 32 into 4 * 8
So the original question = 1 / 4 / 0.05/0.25/8/0.2 = = 1 △ (4x0.05) × (8x0.25) × 0.2
=1÷0.2÷2÷0.2
=12.5 question: A and B are 910 meters apart. A and B walk back and forth from a to B in the same direction at the same time. A travels 80 meters per minute, B travels 60 meters per minute. How many meters is the distance between the second meeting place and the first meeting place?
A: because a and B walk back and forth from a to B in the same direction at the same time, a is faster than B, so the first time they meet must be that they have just walked a lap.
A. B: the distance between the two places is 910 meters, one circle is 910 * 2
910 * 2 / (80 + 60) = 13 (minutes)
The second meeting must be two people's journey, just two laps
60*13-(910-60*13)*2
=780-260
=520(M)
Because B did not walk 910 meters when he first met, B walked to the road for the second time, as shown in the figure: 1 is the place where he walked for the first time. It's the second time to get to the road. Between 2 and 1 is the required answer
B:
B＿＿1＿＿2＿＿A
←←←
→→→→→
As shown in the picture: B's second journey is the journey that he did not finish for the first time * 2 + the distance between the place where they met for the second time and the place where they met for the first time
A: the distance between their second meeting and their first meeting is 520 meters. （1.25*17.6）+（36÷0.8）+（2.64+12.5） （1.25*17.6）+（36÷0.8）+（2.64*12.5）
=1.25*17.6+1.25*28.8/0.8+0.264*1.25
=1.25(17.6+36+0.264)
=1.25*6733/125=67.33
Q: seven tree species in six rows, three in each row, how to plant them? A: it's simple. First place three trees in an equilateral triangle, then place three trees in the middle of each side, and the remaining one in the center of the triangle. Do you count six lines? Three lines are the three sides of the triangle, so that three lines are the three heights of the triangle. Q: four people are pigs. In a certain year, the age product of four people is 15925. Then the ages of these four people from small to large are (). A: simple! The quality factor of 15925 is: 15925 = 5 × 5 × 7 × 7 × 13
15925 = 13 × (5 × 5) × (7 × 7)
The ages of these four people from small to large are: 1.13.25.49. Q: if two arithmetic sequences 5, 8, 11... And 3, 7, 11... Have 100 items, how many of them are the same? The two sequences can be described as 3N + 2 and 4m-1, and the values of N and m are from 1 to 100
2 + 3N = 4m-1, then get 4m = 3 (n + 1). We can see that when m is a multiple of three, the equation will hold. So there are 33 items from 3 to 99. Ha ha, if this solution is wrong (*^__ ^*(hee hee Because the value of n is over 100 at this time. M can only get 75, so there are only 25 items.
A: it can be seen from the equation that since 11 is the same term, one tolerance is 3 and the other is 4, then the same term will appear every time the least common multiple of two tolerances passes. The least common multiple is 12. Then the 100th number of the first sequence is 302, and the 100th number of the second sequence is 399. Well, we must take the smaller one, that is, (302-11) / 12 = 24 more than 3. Then there are 24 identical terms after 11. Plus the initial 11, that's 25.
1. 3/7 × 49/9 - 4/3
2. 8/9 × 15/36 + 1/27
3. 12× 5/6 – 2/9 ×3
4. 8× 5/4 + 1/4
5. 6÷ 3/8 – 3/8 ÷6
6. 4/7 × 5/9 + 3/7 × 5/9
7. 5/2 -（ 3/2 + 4/5 ）
8. 7/8 + （ 1/8 + 1/9 ）
9. 9 × 5/6 + 5/6
10. 3/4 × 8/9 - 1/3
11. 7 × 5/49 + 3/14
12. 6 ×（ 1/2 + 2/3 ）
13. 8 × 4/5 + 8 × 11/5
14. 31 × 5/6 – 5/6
15. 9/7 - （ 2/7 – 10/21 ）
16. 5/9 × 18 – 14 × 2/7
17. 4/5 × 25/16 + 2/3 × 3/4
18. 14 × 8/7 – 5/6 × 12/15
19. 17/32 – 3/4 × 9/24
20. 3 × 2/9 + 1/3
21. 5/7 × 3/25 + 3/7
22. 3/14 ×× 2/3 + 1/6
23. 1/5 × 2/3 + 5/6
24. 9/22 + 1/11 ÷ 1/2
25. 5/3 × 11/5 + 4/3
26. 45 × 2/3 + 1/3 × 15
27. 7/19 + 12/19 × 5/6
28. 1/4 + 3/4 ÷ 2/3
29. 8/7 × 21/16 + 1/2
30. 101 × 1/5 – 1/5 × 21
1. Mental arithmetic
(1)58+42= (2)87－45= (3)125×8=
(4)50×12= (5)804÷4= (6)134＋66=
(7)1000－98= (8)720÷5= (9)0÷47=
2. First fill in the operation order of the following questions, and then calculate the number.
(1)168+36－36+32=
(2)153－5×14+83=
(3)50×5÷50×5=
3. Judgment: mark "√" for right and "×" for wrong
(1) 13 × 15 and 15 × 13 have the same meaning. ()
(2) The calculation result of 3000 ／ 425 ／ 8 must be less than that of 3000 ／ (425 × 8). ()
(3) The product of two factors is 800. If one factor is constant and the other factor is reduced by 20 times, then the product is 40. ()
(4) Formula: "750 △ 25 + 35 × 2" means the quotient of 750 divided by 25; plus 2 times of 35, what is the sum? ()
(5)24×25=6×4×25=6+100=106( )
4. Simple calculation method
(1)3786－499
(2)32×25×125
(3)1653－338－662
(4)7987+350+2013+450
(5)38×38+62×38
(6)452+99×452
(7)201×79
(8)50×125×4×8
5. Calculate the following questions:
(1)340×(120－40÷8)
(2)45×(720－1957÷19)
(3)86+[4500+(2088÷36)÷2]
(4)396×[74－(4875÷15－13×21)]
(5)[1054－(174－168)]÷8
(6)6048÷[(107－99)×9]
6. Use the comprehensive formula
(1) What is the quotient of 42 minus 28 divided by 14?
(2) What's the sum of 840 minus 480 divided by 240, plus 162?
(3) 258 plus the sum of 42 times 185 minus 158