What is the sum of the first 18 numbers in a series of numbers arranged into 1,1,2,2,3,1,1,2,2,3?

Five numbers have one cycle, 18 numbers have three cycles plus 1,1,2
So sum = 3 * 9 + 4 = 31

To prove that f (n) = (2n + 7) 3 ^ n + 9 can be divisible by 36 when n ∈ n

Mathematical induction
n=1:f(n)=9*3+9=36
n=2:f(n)=11*(3^2)+9=108=36*3
...
N = k: F (n) = (2k + 7) * 3 ^ k + 9 assuming divisible by 36
n=k+1:f(n)=(2k+9)*(3^(k+1))+9
=3*(2k+9)*3^k+9
=3*(2k+7)*3^k+9+3*2*3^k
=2*(2k+7)^3^k+((2k+7)*3^k+9)+2*3^(k+1)
=(3^k)*(4k+14+6)+ ((2k+7)*3^k+9)
In this way, the former is obviously divisible by 36, and the latter is assumed in the previous step, so f (K + 1) can be divisible by 36
So f (n) can be divisible by 36
Mathematical induction
1. Prove that the first item is true
2. Suppose item n holds
3. Prove that item n + 1 is true

What symbol does 8 3 use to equal 24
add , subtract , multiply and divide

8/（3-8/3）=24

We know that the absolute value of a positive number is itself, the absolute value of a negative number is only its opposite number, and the absolute value of 0 is still 0
When m is greater than or equal to 0, the absolute value of M = (); when m is less than 0, the absolute value of M = 9 () (fill in the blanks with the formula containing m)
2. From the above, if M-N is regarded as a whole, then when M-N ≥ 0, M-N= When M-N ＜ 0, M-N ＜ 0=
3. The approximate positions of rational numbers a, B and C on the number axis are shown in the figure
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b a o c
Try to simplify a + B + C - a-C

1. The absolute value of a positive number is itself, the absolute value of a negative number is only its opposite number, and the absolute value of 0 is still 0, which is expressed as follows: when m is greater than or equal to 0, the absolute value of M = (m); when m is less than 0, the absolute value of M = 9 (- M / 9). 2

Xiao Ming read a story book. On the first day, he read one third less than on the second day. On the second day, he read five more pages than on the first day. How many pages did he read on the second day?

15 pages

This paper discusses the root of the equation X2 - (m-2) x + M-4 = 0. It is known that the lengths of two sides of the triangle are 1 and 2, and the third side is the root of the equation x2-3x + 2 = 0?

The equation △ = (m-2) & # 178; - 4 (M-4) = (M-4) & # 178; + 4 > 0 has two different roots
x2-3x+2=0 ∴x=1,x=2
∵ the lengths of the two sides of the triangle are 1 and 2 ∵ the third side should be greater than 1 and less than 3 ∵ x = 2
Ψ perimeter = 5

It is known that it takes 4 hours for a bus to complete the whole journey and 3 hours for a truck to complete the whole journey. How many km is the distance between a and B?

It takes 4 hours for a passenger car to complete the whole journey, which means 1 / 4 of the whole journey per hour (passenger car speed). It takes 3 hours for a freight car to complete the whole journey, which means 1 / 3 of the whole journey per hour (freight car speed). When two cars meet, the time taken by two cars is equal. Then the distance ratio of two cars is equal to the speed ratio = 1 / 4:1 / 3 = 3:4

If (3a-2b) x is of the second power + ax + B = 0, and X has a unique solution, then x =?
Write down the process or reason

Solution
∵ is a linear equation of one variable
∴3a-2b=0
And a ≠ 0
∴b=3a/2
The equation becomes ax + 3A / 2 = 0
∴ax=-3a/2
∵a≠0
∴x=-3/2

During the summer vacation, in order to experience life, the Xiaozhang family plan to travel by car every day. If the car travels 19 kilometers more every day than the original plan, it takes 8 days and more than 2200 kilometers; if the car travels 12 kilometers less than the original plan, it takes more than 9 days to travel the same journey
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Excuse me, why am I wrong in doing this?
（19+x）x8＞2200
（x-12）x9＜2200
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The teacher said:
（19+x）x8＞2200
（x-12）x9＜（19+x）x8
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Second question:
In order to realize the balanced development of regional education, our city plans to transform all the weak schools of a and B in a county. According to the budget, a total of 15.75 million yuan is needed. A total of 2.3 million yuan is needed to transform a class a school and two class B schools, and 2.05 million yuan is needed to transform two class a schools and one class B school
(1) How many million yuan are needed to transform a class a school and a class B school?
(2) Our city plans to transform six a and b schools in the county this year, and the transformation funds will be shared by the state finance and the local finance. If the transformation funds allocated by the state finance this year are not more than 4 million yuan, and the transformation funds invested by the local finance are not less than 700000 yuan, the transformation funds of the county will not be less than 700000 yuan, Among them, the local finance invested 100000 yuan and 150000 yuan respectively in the reform of a and b schools?
(2) If there are x class a schools to be transformed this year, there will be (6-x) class B schools to be transformed
According to the meaning of the title:
50x+70(6-x)≤400
10x+15(6-x)≥70
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Excuse me, in 50x + 70 (6-x) ≤ 400, how did 50 and 70 come from?

For example, if the value of (19 + x) X8 is 100000, then (X-12) x9 should be less than 100000

How much is three quarters plus one third minus three sixths?

3/4+1/3-3/6=3/4-1/6=7/12

What is the sum of the first 18 numbers in a series of numbers arranged into 1,1,2,2,3,1,1,2,2,3?