The sum formula of the first n terms of equal difference and equal ratio sequence I forgot to take home my homework from the new textbook The idea of equal difference comes to mind. It's equal

The sum formula of the first n terms of equal difference and equal ratio sequence I forgot to take home my homework from the new textbook The idea of equal difference comes to mind. It's equal

Sn = (a1 + an) n / 2 A1 is the first term and an is the last term
The first tolerance is (a1 + 2) Sn / D = 1
Summation formula of equal ratio sequence
When Q ≠ 1, Sn = A1 (1-Q ^ n) / (1-Q) = (A1 anq) / (1-Q)
When q = 1, Sn = Na1
(A1 is the first term, an is the nth term, D is the tolerance, q is the equal ratio)
sn=a1*(1-qn)/(1-q)=(a1-an*q)/(1-q)
S=N*A1+N*(N-1）*D/2
Equal ratio:
A1 * (n-th power of 1-Q) / (1-Q) / stands for division sign
Hope to help you!!
On all the formulas and variations of the sequence of equal difference and equal ratio
And the variants. All of them
Equal difference: an = a1 + (n-1) d
Sn=n*(a1+an)/2
Sn=A1*n+n*(n-1)d/2
Equal ratio: an = the (n-1) power of A1 * q
Sn=(a1-an*q)/（1-q）
Sn = A1 (power n of 1-Q) / (1-Q)
A1 is the first item, an is a specific item, and Sn is the sum of all items
A1 = 1, an + 1 = (1 / 2) an + N, n is odd number; an-2n, n is even number, and BN = a2n-2 (1) prove that BN is equal ratio sequence and general term formula, (2) sum s
Sum s2n + 1 = a1 + A2 + a3 + a2n+a2n+1
It's too inconvenient to type the formula. In the screenshot, the common ratio of BN is 1 / 2, which is a clerical error. However, the following calculation uses 1 / 2, which is right
A division problem,
698 divided by (1 + 2 / 1) divided by (1-7 / 1) divided by (1-9 / 3)
698 divided by (1 + 2 / 1) divided by (1-7 / 1) divided by (1-9 / 3)
=698 divided by 3 / 2 divided by 6 / 7 divided by 6 / 9
=698 times 2 / 3 times 7 / 6 times 3 / 2
=814 1 / 3
three hundred and forty-nine-thirds
In the physical formula s = 1 / 2at ^ 2, s is distance, a is acceleration, t is time, if s = 10, a = 5, t =?
Substituting s and a into the formula, we can get the following results
10=1/2*5*t^2
=>t^2=4
=>T = 2 (time cannot be negative)
Twenty five questions about the addition and subtraction of integral in the first grade of junior high school
3ab-4ab+8ab-7ab+ab=______ .
4．7x-(5x-5y)-y=______ .
5．23a3bc2-15ab2c+8abc-24a3bc2-8abc=______ .
6．-7x2+6x+13x2-4x-5x2=______ .
7．2y+(-2y+5)-(3y+2)＝______ .
11．(2x2-3xy+4y2)+(x2+2xy-3y2)=______ .
12．2a-(3a-2b+2)+(3a-4b-1)=______ .
13．-6x2-7x2+15x2-2x2＝______ .
14．2x-(x+3y)-(-x-y)-(x-y)＝______ .
16．2x+2y-[3x-2(x-y)]=______ .
17．5-(1-x)-1-(x-1)=______ .
18．( )+(4xy+7x2-y2)=10x2-xy．
19．(4xy2-2x2y)-( )=x3-2x2y+4xy2+y3．
21. Given a = x3-2x2 + x-4, B = 2x3-5x + 3, calculate a + B=______ .
22. Given a = x3-2x2 + x-4, B = 2x3-5x + 3, calculate a-b=______ .
23. If a = - 0.2, B = 0.5, the value of the algebraic formula - (| A2B | - | AB2 |) is______ .
25. Subtract 3m4-m3-2m + 5 from a polynomial to get - 2m4-3m3-2m2-1, then the polynomial is equal to______ .
26．-(2x2-y2)-[2y2-(x2+2xy)]=______ .
27. If - 3a3b2 and 5ax-1by + 2 are of the same kind, then X=______ ,y=______ .
28．(-y+6+3y4-y3)-(2y2-3y3+y4-7)＝______ .
29. The result of simplifying the algebraic expression 4x2 - [7x2-5x-3 (1-2x + x2)] is______ .
30．2a-b2+c-d3=2a+( )-d3=2a-d3-( )=c-( )．
31．3a-(2a-3b)+3(a-2b)-b=______ .
32. The reduced algebraic formula X - [y-2x - (x + y)] is equal to______ .
33．[5a2+( )a-7]+[( )a2-4a+( )]=a2+2a+1．
34．3x-[y-(2x+y)]=______ .
35. Simplify | 1-x + y | - | X-Y | (where x ＜ 0, y ＞ 0) to be equal to______ .
36. It is known that x ≤ y, x + Y - | X-Y|=______ .
37. Given x < 0, y < 0, simplify | x + y | - | 5-x-y|=______ .
38．4a2n-an-(3an-2a2n)＝______ .
39. If a polynomial is added with - 3x2y + 2x2-3xy-4, then
2x2y+3xy2-x2+2xy,
Then the polynomial is______ .
40．-5xm-xm-(-7xm)+(-3xm)=______ .
41. When a = - 1, B = - 2,
[a-(b-c)]-[-b-(-c-a)]＝______ .
43. When a = - 1, B = 1, C = - 1,
-[b-2(-5a)]-(-3b+5c)＝______ .
44．-2(3x+z)-(-6x)+(-5y+3z)=______ .
45．-5an-an+1-(-7an+1)+(-3an)＝______ .
46．3a-(2a-4b-6c)+3(-2c+2b)=______ .
48．9a2+[7a2-2a-(-a2+3a)]=______ .
50. When 2y-x = 5, 5 (x-2y) 2-3 (- x + 2Y) - 100=______ .
．(4x2-8x+5)-(x3+3x2-6x+2)．
72．(0.3x3-x2y+xy2-y3)-(-0.5x3-x2y+0.3xy2)．
73．-{2a2b-[3abc-(4ab2-a2b)]｝．
74．(5a2b+3a2b2-ab2)-(-2ab2+3a2b2+a2b)．
75．(x2-2y2-z2)-(-y2+3x2-z2)+(5x2-y2+2z2)．
76．(3a6-a4+2a5-4a3-1)-(2-a+a3-a5-a4)．
77．(4a-2b-c)-5a-[8b-2c-(a+b)]．
78．(2m-3n)-(3m-2n)+(5n+m)．
79．(3a2-4ab-5b2)-(2b2-5a2+2ab)-(-6ab)．
80．xy-(2xy-3z)+(3xy-4z)．
81．(-3x3+2x2-5x+1)-(5-6x-x2+x3)．
83．3x-(2x-4y-6x)+3(-2z+2y)．
84．(-x2+4+3x4-x3)-(x2+2x-x4-5)．
85. If a = 5a2-2ab + 3B2, B = - 2B2 + 3ab-a2, calculate a + B
86. Given a = 3a2-5a-12, B = 2A2 + 3a-4, find 2 (a-b)
87．2m-{-3n+[-4m-(3m-n)]｝．
88．5m2n+(-2m2n)+2mn2-(+m2n)．
89．4(x-y+z)-2(x+y-z)-3(-x-y-z)．
90．2(x2-2xy+y2-3)+(-x2+y2)-(x2+2xy+y2)．
92．2(a2-ab-b2)-3(4a-2b)+2(7a2-4ab+b2)．
93.2x2-｛-3x-[4x2-(3x2-x)+(x-x2)]｝．
94：-(7x-y-2z)-｛[4x-(x-y-z)-3x+z]-x｝．
95：(+3a)+(-5a)+(-7a)+(-31a)-(+4a)-(-8a)．
96：a3-(a2-a)+(a2-a+1)-(1-a4+a3)．
97．4x-2(x-3)-3[x-3(4-2x)+8]．
3.ab-4ab+8ab-7ab+ab=______ .
4．7x-(5x-5y)-y=______ .
5．23a3bc2-15ab2c+8abc-24a3bc2-8abc=______ .
6．-7x2+6x+13x2-4x-5x2=______ .
7．2y+(-2y+5)-(3y+2)＝______ .
11. (2x2-3xy + 4y2) + (x2 + 2x... Expansion)
3.ab-4ab+8ab-7ab+ab=______ .
4．7x-(5x-5y)-y=______ .
5．23a3bc2-15ab2c+8abc-24a3bc2-8abc=______ .
6．-7x2+6x+13x2-4x-5x2=______ .
7．2y+(-2y+5)-(3y+2)＝______ .
11．(2x2-3xy+4y2)+(x2+2xy-3y2)=______ .
12．2a-(3a-2b+2)+(3a-4b-1)=______ .
13．-6x2-7x2+15x2-2x2＝______ .
14．2x-(x+3y)-(-x-y)-(x-y)＝______ .
16．2x+2y-[3x-2(x-y)]=______ .
17．5-(1-x)-1-(x-1)=______ .
18．( )+(4xy+7x2-y2)=10x2-xy．
19．(4xy2-2x2y)-( )=x3-2x2y+4xy2+y3．
21. Given a = x3-2x2 + x-4, B = 2x3-5x + 3, calculate a + B=______ .
22. Given a = x3-2x2 + x-4, B = 2x3-5x + 3, calculate a-b=______ .
23. If a = - 0.2, B = 0.5, the value of the algebraic formula - (| A2B | - | AB2 |) is______ .
25. Subtract 3m4-m3-2m + 5 from a polynomial to get - 2m4-3m3-2m2-1, then the polynomial is equal to______ .
26．-(2x2-y2)-[2y2-(x2+2xy)]=______ .
27. If - 3a3b2 and 5ax-1by + 2 are of the same kind, then X=______ ，y=______ .
28．(-y+6+3y4-y3)-(2y2-3y3+y4-7)＝______ .
29. The result of simplifying the algebraic expression 4x2 - [7x2-5x-3 (1-2x + x2)] is______ .
30．2a-b2+c-d3=2a+( )-d3=2a-d3-( )=c-( )．
31．3a-(2a-3b)+3(a-2b)-b=______ .
32. The reduced algebraic formula X - [y-2x - (x + y)] is equal to______ .
33．[5a2+( )a-7]+[( )a2-4a+( )]=a2+2a+1．
34．3x-[y-(2x+y)]=______ .
35. Simplify | 1-x + y | - | X-Y | (where x ＜ 0, y ＞ 0) to be equal to______ .
36. It is known that x ≤ y, x + Y - | X-Y|=______ .
37. Given x < 0, y < 0, simplify | x + y | - | 5-x-y|=______ .
38．4a2n-an-(3an-2a2n)＝______ .
39. If a polynomial is added with - 3x2y + 2x2-3xy-4, then
2x2y+3xy2-x2+2xy，
Then the polynomial is______ .
40．-5xm-xm-(-7xm)+(-3xm)=______ .
41. When a = - 1, B = - 2,
[a-(b-c)]-[-b-(-c-a)]＝______ .
43. When a = - 1, B = 1, C = - 1,
-[b-2(-5a)]-(-3b+5c)＝______ .
44．-2(3x+z)-(-6x)+(-5y+3z)=______ .
45．-5an-an+1-(-7an+1)+(-3an)＝______ .
46．3a-(2a-4b-6c)+3(-2c+2b)=______ .
48．9a2+[7a2-2a-(-a2+3a)]=______ .
50. When 2y-x = 5, 5 (x-2y) 2-3 (- x + 2Y) - 100=______ .
．(4x2-8x+5)-(x3+3x2-6x+2)．
72．(0.3x3-x2y+xy2-y3)-(-0.5x3-x2y+0.3xy2)．
73．-{2a2b-[3abc-(4ab2-a2b)]｝．
74．(5a2b+3a2b2-ab2)-(-2ab2+3a2b2+a2b)．
75．(x2-2y2-z2)-(-y2+3x2-z2)+(5x2-y2+2z2)．
76．(3a6-a4+2a5-4a3-1)-(2-a+a3-a5-a4)．
77．(4a-2b-c)-5a-[8b-2c-(a+b)]．
78．(2m-3n)-(3m-2n)+(5n+m)．
79．(3a2-4ab-5b2)-(2b2-5a2+2ab)-(-6ab)．
80．xy-(2xy-3z)+(3xy-4z)．
81．(-3x3+2x2-5x+1)-(5-6x-x2+x3)．
83．3x-(2x-4y-6x)+3(-2z+2y)．
84．(-x2+4+3x4-x3)-(x2+2x-x4-5)．
85. If a = 5a2-2ab + 3B2, B = - 2B2 + 3ab-a2, calculate a + B
86. Given a = 3a2-5a-12, B = 2A2 + 3a-4, find 2 (a-b)
87．2m-{-3n+[-4m-(3m-n)]｝．
88．5m2n+(-2m2n)+2mn2-(+m2n)．
89．4(x-y+z)-2(x+y-z)-3(-x-y-z)．
90．2(x2-2xy+y2-3)+(-x2+y2)-(x2+2xy+y2)．
92．2(a2-ab-b2)-3(4a-2b)+2(7a2-4ab+b2)．
93.2x2-｛-3x-[4x2-(3x2-x)+(x-x2)]｝．
94：-(7x-y-2z)-｛[4x-(x-y-z)-3x+z]-x｝．
95：(+3a)+(-5a)+(-7a)+(-31a)-(+4a)-(-8a)．
96：a3-(a2-a)+(a2-a+1)-(1-a4+a3)．
97.4x-2 (x-3) - 3 [x-3 (4-2x) + 8]
1.3ab-4ab+8ab-7ab+ab=______ .
2．7x-(5x-5y)-y=______ .
3．23a3bc2-15ab2c+8abc-24a3bc2-8abc=______ .
4．-7x2+6x+13x2-4x-5x2=______ .
5．2y+(-2y+5)-(3y+2)＝______ .
6. (2x2-3xy + 4y2) + (x2 + 2x... Expansion)
1.3ab-4ab+8ab-7ab+ab=______ .
2．7x-(5x-5y)-y=______ .
3．23a3bc2-15ab2c+8abc-24a3bc2-8abc=______ .
4．-7x2+6x+13x2-4x-5x2=______ .
5．2y+(-2y+5)-(3y+2)＝______ .
6．(2x2-3xy+4y2)+(x2+2xy-3y2)=______ .
7．2a-(3a-2b+2)+(3a-4b-1)=______ .
8．-6x2-7x2+15x2-2x2＝______ .
9．2x-(x+3y)-(-x-y)-(x-y)＝______ .
10．2x+2y-[3x-2(x-y)]=______ .
11．5-(1-x)-1-(x-1)=______ .
12．( )+(4xy+7x2-y2)=10x2-xy．
13．(4xy2-2x2y)-( )=x3-2x2y+4xy2+y3．
14. Given a = x3-2x2 + x-4, B = 2x3-5x + 3, calculate a + B=______ .
15. Given a = x3-2x2 + x-4, B = 2x3-5x + 3, calculate a-b=______ .
16. If a = - 0.2, B = 0.5, the value of the algebraic formula - (| A2B | - | AB2 |) is______ .
17. Subtract 3m4-m3-2m + 5 from a polynomial to get - 2m4-3m3-2m2-1, then the polynomial is equal to______ .
18．-(2x2-y2)-[2y2-(x2+2xy)]=______ .
19. If - 3a3b2 and 5ax-1by + 2 are of the same kind, then X=______ ，y=______ .
20．(-y+6+3y4-y3)-(2y2-3y3+y4-7)＝______ . put it away
Division of rational numbers
1.25 ± (- 0.5) ± (- 5 / 8)
-18 ／ 3.25 ／ - 2 and a quarter
(- three fifths) × (- 3 and a half) △ (- 1 and a quarter) △ 3
-97 of 99 × (- 98)
Question 1 = 5 / 4 * (- 2) * (- 8 / 5) = 4
Question 2 = = (- 18) * 4 / 13 * (- 4 / 9) = 32 / 117
3=（-3/5）*7/2*（-4/5）*1/3=14/25
4==99*98+97=（100-1）*98+97=9800-98+97=9799
Acceleration is measured in meters per second. Is displacement divided by the square of time equal to acceleration
No, it's the concept of differential. It's the second derivative of displacement with respect to time
Urgent first day on mathematics mixed operation, solving equations, simplifying evaluation, application problems, 25 each
No answer, please. Hurry up
On the first day of the random ah ~ moderate difficulty to solve equation problems
Give a piece of pancake to 11 children. Only 6 cuts are allowed. How many pieces can each child get at most
Simplification by long division
How to use long division to factorize the following formula
6X ^ 4-20x ^ 2-3x + 8 divided by 3x + 3
(reduced to the simplest form)
2x^3-2x^2-14/3x+8/3
3x+3|6x^4+0x^3-20x^2-3x+8
-(6x^4+6x^3)
——————————————
-(-6x^3-6x^2)
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That is, the simplest formula of 6x ^ 4-20x ^ 2-3x + 8 divided by 3x + 3 is 2x ^ 3-2x ^ 2-14 / 3x + 8 / 3