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$$C_1$$, $$C_2$$, $$C_3$$, ......,$$C_K$$, ......

The sequence shown above is defined by $$C_1$$=7 and $$C_{K+1}$$= $$\frac{1}{7}$$ $$C_K$$, for each positive integer k

Quantity A

$$C_{12}$$

Quantity B

($$49^{7}$$)$$C_{26}$$


A ball drops from above to the ground and bounced back to $$\frac{1}{3}$$ of its original height. If the ball is at first 50 feet from the ground, then by how many times will the height of the ball drop below 1 feet?
-1, 2, -3, 4, ... , a_n, ... , -99, 100

In the finite sequence, $$a_n$$=$$(-1)^{n}$$*n for all integers n between 1 and 100, inclusive.

Quantity A

The sum of the terms in the sequence

Quantity B

51


A list of numbers could be summarized into $$S_{n}=n•(-1)^{n}$$ (n is a positive integer), and $$S_{1}=-1$$. What`s the sum of $$S_{1}$$, $$S_{2}$$, $$S_{3}$$, ......, $$S_{497}$$, $$S_{498}$$, $$S_{499}$$?
$$a_1$$=4, $$a_2$$=-3, $$a_3$$=7. If for any integer n greater than 3, $$a_n$$=|$$a_n$$-1-$$a_n$$-2|, then what`s $$a_{35}$$?
How many different positive three-digit integers are there that have an odd hundreds digit?
How many three-digit positive numbers are divisible by 5 and have a hundreds digit which is an odd number?
Set A={1, 2, 3}

Set B={1, 2, 3, 4}

Quantity A

The number of different four-digit integers that can be formed by elements from Set A (all the elements can be used by more than once)

Quantity B

The number of different three-digit integers that can be formed by elements from Set B (all the elements can be used by more than once)


In a city, car plates are composed of 7 digits. Among them, the former digits should all be letters from the 26 alphabets, while the latter digits should all be numbers from 0 to 9.

x: The number of possible different car plates when choosing four letters(A-Z) and three numbers(0-9),numbers and letters can be used more than once.

y: The number of possible different car plates when choosing four letters(A-Z) and three numbers(0-9),numbers and letters can not be used more than once.

z: The number of possible different car plates when choosing three letters(A-Z) and four numbers(0-9),numbers and letters can be used more than once.

Quantity A

x-y

Quantity B

z


If 3 integers are randomly selected out of 1, 2, 3, 4, 5 (no repeated numbers are allowed) to form a positive three-digit integer, then how many different integers can be formed?


If it is not allowed to pass through any vertex and intersection repeatedly, how many ways are there to go from A to B along the line segment?
Ordered pairs (x, y), where1 ≤ y < x ≤ 8, x and y are both integers

How many different pairs are there?
A number is to be randomly selected from the integers from 1 through 87.

Quantity A:The probability that the number selected will have a units digit of 6

Quantity B:The probability that the number selected will have a tens digit of 6


Several 0 and 1 are arranged in a 10*10 palace as follows. Among all the number 0, what is the probability that the selected 0 is located where the number of 0 in that row is odd while the number of 0 in that column is also odd?

Give your answer as a fraction.
In a box of red, blue and green balls, if the ratio of red to blue is 2:3, the ratio of blue to green is 4:3, then what ratio of all balls in the box are blue ones?

Give your answer as a fraction.
125w+25x+5y+z=264, w, x, y and z are integers that are no less than 0 and no greater than 5. What is the sum of w+x+y+z?

Indicate all such values.
What is the reminder when $$ (345,606)^{2}$$ is divided by 20?
If the sum of two numbers is 10, what is the greatest possible value of the product of the two numbers?
Which of the following numbers satisfy their sum of reciprocals is either less than $$\frac{1}{3}$$ or greater than $$\frac{1}{2}$$ ?

Indicate all such numbers.
x≠0, y≠0

|x|+|y|=|x+y|

Which of the following statements must be true?

Indicate all such statements.

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