The nth number can be expressed as

The nth number can be expressed as

3(n-1) n>1

Find the law - 3, - 1,1,3,5,7,9 The nth number is_____
Find the rule 5,3,1, - 1, - 3, - 5 The nth number is_____

1. The nth number = 2n-52, the nth number = - 2n + 7

Charcoal + oxygen →?

Ignite
Charcoal + oxygen - → carbon dioxide
The "ignition" should be written above the arrow. Don't forget the reaction conditions!

If there is a quadrilateral in which the sum of squares of one set of opposite sides is equal to the sum of squares of another set of opposite sides, it is called an equal sum of squares quadrilateral
In trapezoidal ABCD, if ad ∥ BC, AC ⊥ BD and perpendicular foot are o, then quadrilateral ABCD is equal square sum quadrilateral. If △ AOD is rotated a degree (0 ⊥ α ⊥ 90) counterclockwise around point O, can quadrilateral ABCD be equal square sum quadrilateral? Please explain the reason

Quadrilateral ABCD can be equal square sum quadrilateral
Company AC, BD, hand over to e
In △ AOD and △ cob,
∠ADO=∠OBC,
∠DAO=∠OCB,
∴△AOD∽△COB,
∴AO/CO=DO/BO,
∵∠AOC=∠DOB=90+∠AOB,
∴△AOC∽△DOB,
∴∠OAC=∠ODB,
In the AOD of right triangle, ∠ oad + ∠ ODA = ∠ oad + ∠ ADB + ∠ BDO = 90
In the triangle AED, ∠ ead + ∠ EDA = ∠ EAO + ∠ oad + ∠ ADB = ∠ BDO + ∠ oad + ∠ ADB = 90
∴∠AED=90°,
By using Pythagorean theorem, we can find that,
AD^2=AE^2+DE^2,BC^2=BE^2+CE^2,
AB^2=AE^2+BE^2,CD^2=CE^2+DE^2,
∴AD^2+BC^2=AB^2+CD^2,
So this quadrilateral is the sum of squares quadrilateral

Sum of squares of three consecutive natural numbers______ The square of a natural number

Let three continuous natural numbers be A-1, a, a + 1, then their sum of squares is (A-1) 2 + A2 + (a + 1) 2 = 3a2 + 2. Obviously, when the sum is divided by 3, the remainder 2 must be obtained. On the other hand, when the natural number is divided by 3, the remainder can only be 0 or 1 or 2, so they can be expressed as one of 3b, 3b + 1, 3b + 2 (B is a natural number), but their square (3b) 2 = 9b2 (3b + 1) 2 = 9b2 + 6B + 1, (3) 2 = 9b2 + 6B + 1 When B + 2) 2 = 9b2 + 12b + 4 = (9b2 + 12b + 3) + 1 is divided by 3, the remainder is either 0 or 1, not 2, so the sum of squares of three continuous natural numbers is not the square of a certain natural number

When n is an integer, prove that the sum of squares of two consecutive integers is equal to the difference of squares of the two integers

This conclusion is wrong!
There is only one case: (± 1) &# 178; + 0 &# 178; = (± 1) &# 178; - 0 &# 178;)

If the sum of the squares of two numbers is equal to the sum of the squares of the other two numbers, is the sum of these two numbers equal to the sum of those two numbers?

There are waiting and waiting
For example, the sum of squares of 0 and 5 and the sum of squares of 3 and 4
The sum of squares of 1 and 2 is equal to the sum of squares of two-thirds root sign 3 and two-thirds root sign 3
All in all, there are many examples

Prove that a number is equal to the sum of the squares of two numbers, and that twice the number is equal to the sum of the squares of two numbers
Proof: if a number can be expressed as the sum of squares of two integers, then twice the number can also be expressed as the sum of squares of two integers.

Let C = a ^ 2 + B ^ 2
Then 2C = 2A ^ 2 + 2B ^ 2
=(a-b)^2+(a+b)^2
Proof of original title

Given that the sum of 2 roots is - 3 and the sum of squares is 29, the equation can be solved

x1²+x2²=29
x1+x2=-3
square
x1²+x2²+2x1x2=9
So 2x1x2 = 9-29 = - 20
x1x2=-10
So x & sup2; - (x1 + x2) x + x1x2 = 0
That is X & sup2; + 3x-10 = 0

Three times of a certain number is 2 larger than half of it. If a certain number is x, then the equation is__________ .
Such as the title

3x-x/2=2