Formula for finding general term of equal ratio sequence By analogy with the arithmetic sequence, if you know the m-th term of the sequence, you can also write the general term formula of the sequence. Then in the arithmetic sequence, if you know the m-th term am, can you also find the general term formula? If you can, please write and prove it

an=am*q^(n-m)
an=a1*q^(n-1)
am=a1*q^(m-1)
an/am=q^[n-1-m+1]=q^(n-m)
an=am^q(n-m)
On the formula of fraction
On the formula of fraction, it's better to be complete
fraction
Section 1 basic concept of fraction
1. Definition: integral a divided by integral B can be expressed in the form of. If Division B contains letters, it is called fraction
Note: a △ B = = a × = a × B-1 = A &; B-1. Sometimes it is written as negative index, i.e. a &; B-1, which is different in form but not in essence
2. Composition: in the fraction, a is called the numerator of the fraction, B is called the denominator of the fraction
3. Meaning: for any fraction, the denominator cannot be 0, otherwise the fraction is meaningless
4. If the denominator is not equal to 0 and the numerator is equal to 0, then the fractional value is 0
Note: the concept of fraction includes three aspects: 1) fraction is the quotient of the division of two integers, in which the numerator is divided and the denominator is divided, and the fractional line acts as a division sign; 2) the denominator of a fraction must contain letters, while the numerator can contain letters or not, which is an important basis for distinguishing integers; 3) in any case, the denominator of a fraction cannot be 0, In other words, the denominator of a fraction is not zero, which is a condition implied in the fraction without any indication
Section 2 basic properties of fraction and its application
5. The basic properties of fraction: the numerator and denominator of fraction multiply or divide by the same integer which is not zero, and the value of fraction remains unchanged
6. Reduction: the reduction of the common factor of the numerator and denominator of a fraction
7. The steps of fraction reduction are as follows: (1) if the numerator and denominator of a fraction are monomials or the product of several factors, their common factors are reduced. (2) if the numerator and denominator of a fraction are polynomials, the numerator and denominator are decomposed into factors respectively, and then the common factors are reduced
Note: extraction method of common factor: coefficient takes the greatest common divisor of numerator and denominator coefficient, letter takes the common letter of numerator and denominator, index takes the minimum index of common letter, which is their common factor
8. The simplest fraction: when the numerator and denominator of a fraction have no common factor, the fraction is called the simplest fraction. In reduction, a fraction is usually reduced to the simplest fraction
9. General division: to change several different denominator fractions into the same denominator fractions with the same value of the original fraction
10. The general division steps of fractions: first, find out the simplest common denominator of the denominators of all fractions, and then change the denominators of all fractions into the simplest common denominator. At the same time, each fraction expands its own numerator according to the multiple of the denominator
Note: the determination method of the simplest common denominator: the coefficient is the product of the least common multiple of each factor coefficient, the highest power of the same letter and the power of a single letter
Note: (1) the basis of reduction and general division are the basic properties of fractions. (2) reduction and general division of fractions are reciprocal operations
Section 3 four operations of fraction
11. The same denominator fraction addition and subtraction rule: denominator unchanged, the addition and subtraction of molecules
12. Different denominator fraction addition and subtraction rule: after general division, it is calculated according to the same denominator fraction addition and subtraction rule
13. The multiplication rule of fractions: use the product of the numerator as the numerator and the product of the denominator as the denominator
14. The division rule of fraction: change the division to its reciprocal and multiply it with the divided
Section 4 fractional equation
15. The meaning of fractional equation: the equation with unknown number in denominator is called fractional equation
16. The solution of fractional equation: ① remove the denominator (multiply both sides of the equation by the simplest common denominator at the same time to transform the fractional equation into an integral equation); ② calculate the value of the unknown according to the steps of solving the integral equation; ③ check the root (the root must be checked after the value of the unknown is calculated, because in the process of transforming the fractional equation into an integral equation, the value range of the unknown is expanded, and the root may be increased)
What is the maximum distance between the point on the circle x ^ 2 + y ^ 2 = 4 and the line 3x-4y + 5 = 0
The distance from the center of circle (0,0) to the straight line d = | 0-0 + 5 | / √ (3 & # 178; + 4 & # 178;) = 1
R=2
So the maximum distance is d + r = 3
On the general term formula of equal ratio sequence
Why is it necessary to use an = sn-sn-1 to find the general term formula of equal ratio sequence
This should only be used in arithmetic sequence
The premise is n > = 2. If the premise is satisfied, it can be used for any sequence. SN: the first n terms and Sn = a1 + A2 + +A (n-1) + ans (n-1): sum of the first n-1 terms s (n-1) = a1 + A2 + +A (n-1) "the sum of the first n terms" minus "the sum of the first n-1 terms" is of course equal to the size of the nth term, that is, an
SN is A1 to an
Sn-1 is a1 + an-1
Subtract to get your formula
No, as long as it's a sequence
Because: SN = a1 + A2 + +an-1+an
sn-1=a1+a2+…… +an-1
So Sn = sn-1
What should be paid attention to in fractional mixing operation? What are the rules
Pay attention to the order of operations; from high-level operations to low-level operations, those with brackets are counted first; pay attention to the symbols
If there are brackets, the brackets will be calculated first, then the square will be calculated, then the multiplication and division will be made, and finally the addition and subtraction will be made
The line 3x-4y-5 = 0 intersects the circle C: (X-2) &# 178; + (Y-1) &# 178; = 25 at two points a and B. find the area of △ ABC
Center (2,1), radius r = 5
Distance from center of circle to straight line d = | 6-4-5 | / 5 = 3 / 5
According to Pythagorean theorem, | ab | = 2 * √ (R ^ 2-D ^ 2) = 2 * √ (25-9 / 25) = 4 / 5 * √ 154
S=1/2*|AB|*d=6/25*√154
The distance from the center of the circle to the straight line is
|6-4-5 | / radical (3 & # 178; + 4 & # 178;) = 3 / 5
The radius of the circle is 5
Using Pythagorean theorem
AB / 2 = radical [5 & # 178; + (3 / 5) &# 178;] = radical (634 / 25)
AB = double root (634 / 25)
Area of △ ABC = 0.5 × 3 / 5 × 2 root (634 / 25)
=12 times root 634
Circle C: (X-2) ^ 2 + (Y-1) ^ 2 = 25
The center of the circle is (2,1) and the radius is r = 5
So the distance from the center of the circle to the straight line is d = | 3 * 2-4 * 1-5 | / √ (3 ^ 2 + 4 ^ 2) = 3 / 5
So AB = √ (5 ^ 2-D ^ 2) = √ (25-9 / 25) = 2 √ 154 / 5
So the area of △ ABC is s = AB * D / 2 = (2 √ 154 / 5) * (3 / 5) / 2 = 3 √ 154 / 25
If you don't understand, please hi me, I wish you a happy study!
Firstly, the distance from O to line is calculated by using the formula of distance from point to line, that is, the height of triangle.
Then the linear equation is brought into the circular equation to get the coordinates of a and B. Then we find the length of AB, which is the base of the triangle.
Finally, we can calculate the area of the triangle.
Let the coordinates of a and B be (x1, Y1), (X2, Y2) respectively
Simultaneous equations 3x-4y-5 = 0 (X-2) &# 178; + (Y-1) &# 178; = 25
Their solution is that the coordinates of points a and B determine the shape of △ ABC and finally calculate the area
Integral equation bivariate linear equation bivariate linear equation bivariate quadratic equation
Their differences, definitions and forms (for example) thank you
A + B = 0, 1 lower
A + 2A = 3A, 2 lower
A square = 2, 3 lower
There's a definition of reading books in the trees,
Binary linear equations: x + y = 10 has two variables. One variable linear equation: x + 5 = 10 is only one variable. Quadratic equation of one variable: the square of X + 5 = 10 means that there is a variable, but it is quadratic, and there can be two X, that is, the positive and negative root sign 5
It's very simple
Equation of degree y with X elements
X unknowns the maximum number of unknowns is y
For example, the square of X and the cubic power of Y are 2 + 3 = 5
The definition of fraction, algorithm
The basic concept of fraction is like a / b. A and B are integers. The integers that contain unknowns in B and B is not equal to 0 are called fractions. A is the numerator of fraction and B is the denominator of fraction. To master the concept of fraction, we should pay attention to: judge whether a formula is a fraction, not whether the formula is a / b form, the key is to satisfy. (1)
What is the positional relationship between the line 3x-4y + 2 = 0 and the circle (x-1) &# 178; + Y & # 178; = 1?
Equation, quadratic equation, one variable, one variable, quadratic equation, one variable, quadratic equation, that is, who contains who?
To draw a circle is 1 yuan once, followed by 1 yuan twice and twice

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