1. Given that {a} is an arithmetic sequence, and A3 = 10, a7 = 42, find A1, D, an, Sn 2. Given that {a} is an equal ratio sequence, and A1 = 1, A3 = 4, find A10, Sn

1. Given that {a} is an arithmetic sequence, and A3 = 10, a7 = 42, find A1, D, an, Sn 2. Given that {a} is an equal ratio sequence, and A1 = 1, A3 = 4, find A10, Sn

Remember an = a1 + (n-1) d to an = am + (n-m) d
So the problem d = (a7-a3) / (7-3) = 32 / 4 = 8
a1=a7+(1-7)d=42-6*8=-6
An = a1 + (n-1) d = - 6 + 8 (n-1) sum of their own push, are substituted on the line;
The number sequence of equal proportion is to the (n-1) power of an = A1 * Q. q is equal to plus or minus 2

Ask for help to write the following mathematical formula specific calculation steps
Solve (A-1 / 2) ^ 2 (a ^ 2 + 1 / 4) ^ 2 (a + 1 / 2) ^ 2 = a ^ 8-1 / 8A ^ 4 + 1 / 256
(- 3 / 4x ^ 6y ^ 3 + 6 / 5x ^ 3Y ^ 4-9 / 10xy ^ 5) divided by 3 / 5xy ^ 3 = - 5 / 4x ^ 5 + 2x ^ 2y-3 / 2Y ^ 2
X^M- 1/2X^m+1 - 1/5X^m + X^m+1 - 2X^m+1 = 4/5X^m- 3/2X^m+1
I find that the book is really concise now~

1. Using the square difference formula, the complete square formula expands (A-1 / 2) ^ 2 (a ^ 2 + 1 / 4) ^ 2 (a + 1 / 2) ^ 2 = (A-1 / 2) ^ 2 * (a + 1 / 2) ^ 2 * (a ^ 2 + 1 / 4) ^ 2 = (a ^ 2-1 / 4) ^ 2 * (a ^ 2 + 1 / 4) ^ 2 square difference formula = (a ^ 4 - 1 / 16) ^ 2 square difference formula = a ^ 8-1 / 8A ^ 4 + 1 / 256 complete square formula

Find a mathematical formula to calculate income
Invest 1000 yuan per month, and the monthly income is 1%

1000（1+1%）^n+1000（1+1%）^（n-1）+…… +1000（1+1%）

Observe the following list of regular numbers: 1 / 3, 2 / 8, 3 / 15, 4 / 24. According to this rule, the nth number is____

1 / (n + 2) or N / {(n + 2) * n}

Use 1, 2, 3, 4, 5, 6, 7, 8, 9 to write the division formula where the divisor with equal quotient is two digits and the divisor is one digit and the number cannot be repeated

21 divided by 3 = 56 divided by 8 = 49 divided by 7 = 7

The problem of point symmetry in space rectangular coordinate system
What are the coordinates of the symmetric point of point a (3, - 2,4) with respect to point B (0,1, - 3)?
Is there any formula?

(x, y, z) for (a, B, c) symmetric point (m, N, q), x + M = 2A, y + n = 2B, Z + q = 2C
Answer (- 3,4, - 10)

Finding the value range of real number k by the intersection of straight line y = KX and hyperbola x ^ 2 / 16 -- y ^ 2 / 9 = - 1

The line y = KX ① intersects the hyperbola x ^ 2 / 16-y ^ 2 / 9 = - 1 ②,
Substituting ① into ② * 144, 9x ^ - 16K ^ x ^ = - 144,
(9-16k^)x^=-144,
X ^ = 144 / (16K ^ - 9), there is a solution,
16k^-9>0,
k^>9/16,
k> 3 / 4 or K

3 () 4 () 5 () 3 = 24 What sign should be filled in the brackets to make the equation hold

3*（4+5）-3=24

a> 1 and a ^ (LGB) = 2 ^ (1 / 4) to find the minimum value of log2 (AB)
Use the knowledge of "arithmetic mean and geometric mean" in the first volume of senior two

A ^ (LGB) = 2 ^ (1 / 4) take the common logarithm on both sides and get LGA * LGB = 1 / 4lg2, so from "arithmetic mean of positive number is greater than geometric mean", (LGA + LGB) / 2 > = (LGA * LGB) ^ (1 / 2) = 1 / 2 * (LG2) ^ 1 / 2, so log2 (AB) = (LGA + LGB) / LG2 > = 1 / (LG2) ^ 1 / 2, the minimum value of log2 (AB) is 1 / (LG2) ^ 1 / 2

Then evaluate (1 + B / A-A / a-b) divided by (1-B / A-A / A + b) to get 3a-2b = 0

In simplification, the numerator and denominator multiply a * (a + b) * (a-b)
Bring in a = 2 * B / 3
Equivalent to (1 + 3 / 2 + 2) / (1 - 3 / 2 - 2 / 5)
= (9/2) / (-9/10)
= -5