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题目内容
During a 7-day period, a plant's height increased half as much each day as it did the day before. What is the ratio of the plant's increase in height on day 4 to its increase in height on day 7?
$$C_1$$, $$C_2$$, $$C_3$$, ......,$$C_K$$, ......

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
$$a_1$$, $$a_2$$, $$a_3$$,......,$$a_{150}$$

The $$n_{th}$$ term if the sequence shown is defined for each integer n from 1 to 150 as follows. If n is odd, then $$a_n$$=$$\frac{(n+1)}{2}$$, and if n is even, then $$a_{n}$$=$$(a_{n-1})^{2}$$. How many integers appear in the sequence twice?
If a sequence is defined by $$a_{n}=n(-1)^{n}$$ for all integers $$n$$ from 1 through 499, what is the sum of all the terms in the sequence?
$$a_k$$ = ($$\frac{1}{k} - \frac{1}{k+1}$$) for any positive integer k.

Quantity A

$$a_3$$+$$a_4$$+$$a_5$$+$$a_6$$+$$a_7$$

Quantity B

$$\frac{1}{8}$$
$$a_1$$=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 the sum of all the terms from $$a_1$$ to $$a_{35}$$?
$$a_1$$=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?
There are 2 different choices of Product A, 4 different choices of Product B and 5 different choices of Product C. In how many ways can these products be selected if either 1 or none of item is selected out of Product A, B, and C, respectively?
A team of two students from an art school is to be selected to represent the school at a national event. The two students will be selected from the students in three classes that have no students in common. The three classes have 10 students, 8 students, and 7 students. If the two students must be selected from different classes, how many teams are possible?
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?
How many integers between 100 and 1,000 have a hundreds digit that is even, a tens digit that is odd, and a non-zero units digit that is divisible by 3?
In a gift box, there are three types of gifts: 4 yoyo balls of different designs, 4 toys of different colors, and 3 candy bars of different flavors. In how many ways can 3 gifts be selected such that each one is out of each type of gift?
If an integer is chosen at random from the integers between 101 and 550, inclusive, what is the probability that the chosen integer will begin with the digit 1, 2 or 3, and end with the digit 4, 5, or 6?
Among 350 card, cards No.100 to No.299 are red. Among all red cards, cards that end with 4, 5, 6, 7, 8, 9 and 0 are round. What is the probability that a red round card is selected when randomly selecting a card from all 350 cards?
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

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