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题目内容
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 $$S_{1}$$, $$S_{2}$$, $$S_{3}$$, ......, $$S_{97}$$, $$S_{98}$$, $$S_{499}$$?
In a sequence, $$a_{1}=4$$, $$a_{2}=2$$. If for any n greater than 2, $$a_{n}=a_{n-1}+a_{n-2}$$, then how many terms in the first 60 terms are multiples of 3?
$$a_1, a_2, a_3,.................a_n,......$$

In the sequence shown, $$a_{1}=4$$, $$a_{2}=2$$, and for all integers n greater than 2, $$a_{n}$$ is equal to the sum of the squares of $$a_{n-1}$$ and $$a_{n-2}$$. How many of the first 60 terms of the sequence are multiples of 3?
The sequence $$a_{1},a_{2},a_{3}.....a_{n}$$....is defined by $$a_{1}=2$$, $$a_{2}$$=3, and $$a_{n}$$=$$(a_{n－1})(a_{n－2})$$ for all integers n greater than 2. What is the value of $$a_{8}$$?
$$a_{1}=2$$，$$a_{2}=5$$
If $$a_{n}=a_{n-1} / a_{n-2}$$，then $$a_{135} =$$?
Give your answer as a fraction.
A positive integer is a palindrome if it reads exactly the same from right to left as it does from left to right. For example, 5 and 66 and 373 are all palindromes. How many palindromes are there between 1 and 1,000, inclusive?
N equals the number of positive 3-digit numbers that contain odd digits only (the same number could be used for more than once).

Quantity A

N

Quantity B

125

Quantity A

The number of 3-digit integers all of whose digits are even (the same number could be used for more than once)

Quantity B

The number of 3-digit integers all of whose digits are odd (the same number could be used for more than once)
S={1, 2, 3}
T={1, 2, 3, 4}

Quantity A

The total number of 4-digit positive integers that can be formed using only the digits in set S

Quantity B

The total number of 3-digit positive integers that can be formed using only the digits in set T
A three-digit code for certain locks uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 according to the following constraints. The first digit cannot be 0 or 1, the second digit must be 0 or 1, and the second and third digits cannot both be 0 in the same code. How many different codes are possible?
Set S = {1, 4, 7, 10}
Set T = {2, 3, 5, 8, 13}
x is a number in set S, and y is a number in set T.
Quantity A: The number of different possible values of the product xy
Quantity B: 20

Mark is supposed to fill three sectors of a garden with a selection of five colors of flowers. The same color could be used, but only twice at most, and not adjacent. In how many ways can the garden be decorated?
$$d$$ is a integer greater than $$1$$.

Quantity A

$$(d^{2})!$$

Quantity B

$$(d!)^{2}$$
Which of the following values of $$x$$ satisfies the equation $$\frac{x}{2}=n!$$ for some positive integer $$n$$?

Quantity A

14!

Quantity B

15!-14!
（51!-50!）÷（50!-49!）=?
Give your answer as a fraction.
The area of a square is 16. If its area increases by 6, then each of its side needs to be how much longer?

If ABCD is a square with area 625, and CEFD is a rhombus with area 500, then the area of the shaded region is?
Note: Figure not drawn to scale

BC//AD//EF, AD=9, BC=3, AB=4, CD=6
If the perimeter of CBEF is the same as DAEF, then the sum of AE+DF is?

Quantity A

The area of the shaded area

Quantity B

15

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