$a_n=2n-3$

$a_n={\displaystyle \frac{n(n-2)}{2}}$

$a_n={\displaystyle \frac{n}{2n+1}}$

$a_n={(-2)}^{n-1}$

30, 28, 26, 24, …

$-1,2,-4,8,\dots$

${\displaystyle \frac{9!}{8!}}$

${\displaystyle \frac{10!}{7!}}$

${\displaystyle \frac{(n+1)!}{n!}}$

${\displaystyle \frac{n!}{(n-2)!}}$

${\displaystyle \sum _{k=1}^4{k}^3}$

${\displaystyle \sum _{j=1}^5{\displaystyle \frac{1}{2j}}}$

${\displaystyle \sum _{k=1}^7{\displaystyle \frac{k+1}{k}}}$

${\displaystyle \sum _{k=1}^5{(-1)}^k{3}^{k+1}}$

$1+{\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{3}}+{\displaystyle \frac{1}{4}}+\cdots +{\displaystyle \frac{1}{50}}$

$2-4+8-16+32$

$11,6,1,-4,\dots$

${\displaystyle \frac{2}{3}},{\displaystyle \frac{5}{6}},1,{\displaystyle \frac{7}{6}},\dots$

$a_n=n^2+4$

$a_n=3n-5$

3, 6, 9, 12, 15, …

5, 9, 13, 17, 21, …

$x,x+1,x+2,x+3,x+4,\dots$

3x, 5x, 7x, 9x, 11x, …

3rd term: 7; 8th term: 17

5th term: $-16;$ 20th term: $-46$

$7+9+11+13+\cdots +37$

${\displaystyle \frac{1}{4}}+{\displaystyle \frac{1}{2}}+{\displaystyle \frac{3}{4}}+1+\cdots +15$

$3,8,13,\dots ;n=40$

$-6,-5.5,-5,\dots ;n=60$

$4,-8,16,-32,\dots$

${\displaystyle \frac{1}{5}},{\displaystyle \frac{1}{10}},{\displaystyle \frac{1}{20}},{\displaystyle \frac{1}{40}},\dots$

${\displaystyle \frac{1}{3}},1,{\displaystyle \frac{5}{3}},9,\dots$

$a_n=2^{-n}$

$16,-4,1,-{\displaystyle \frac{1}{4}},\dots$

$-{\displaystyle \frac{5}{6}},-{\displaystyle \frac{1}{3}},-{\displaystyle \frac{2}{15}},-{\displaystyle \frac{4}{75}},\dots$

$a_{10}$ when $a_1=2,r=3$

$a_{12}$ when $a_1=-2,r={\displaystyle \frac{3}{2}}$

${\displaystyle \frac{1}{10}},{\displaystyle \frac{1}{5}},{\displaystyle \frac{2}{5}},{\displaystyle \frac{4}{5}},\dots ;n=12$

$2,-1,{\displaystyle \frac{1}{2}},-{\displaystyle \frac{1}{4}},\dots ;n=10$

${\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{6}}+{\displaystyle \frac{1}{18}}+{\displaystyle \frac{1}{54}}+\cdots$

$-5-2-{\displaystyle \frac{4}{5}}-{\displaystyle \frac{8}{25}}-\dots$

${\displaystyle \sum _{i=1}^{\infty }{\left({\displaystyle \frac{3}{5}}\right)}^i}$

${\displaystyle \sum _{i=1}^{\infty }7{(-{\displaystyle \frac{1}{4}})}^i}$

${\displaystyle \sum _{k=1}^n{2}^k=2^{n+1}-2}$

${\displaystyle \sum _{k=1}^{n}k(k+1)={\displaystyle \frac{n(n+1)(n+2)}{3}}}$

$\left(\begin{array}{c}12\\ 7\end{array}\right)$

$\left(\begin{array}{c}11\\ 0\end{array}\right)$

${(x-3)}^4$

${({\displaystyle \frac{x}{2}}+2)}^6$

${(x+2)}^{12};$ term containing $x^5$

${(x+2y)}^{12};$ term containing $x^7$

How many different numbers can be written with the digits 1, 2, 3, and 4 if no digit may be repeated?

How many ways can horses finish in first, second, and third place in a ten-horse race?

How many ways can seven people line up at a ticket ­window? 

In a building with seven entrances, how many ways can you enter the building and leave by a different entrance?

How many ways can five movies be listed on a display ­(vertically, one movie per line)?

How many different amounts of money can you make with a nickel, a dime, a quarter, and a half-dollar?

How many ways can three candies be taken from a box of ten candies?

How many ways can 2 face cards be drawn from a standard 52-card deck?

How many ways can 2 shirts and 3 pairs of pants be chosen from 12 shirts and 8 pairs of pants?

How many doubles teams can be formed from eight tennis players?

In how many distinguishable ways can the letters of the word R E I T E R A T E be arranged?

A bookshelf has room for four books. How many different arrangements can be made on the shelf from six available books?

Four silver dollars, all with different dates, are randomly arranged on a horizontal display. What is the probability that the two with the most recent dates will be next to each other?

A jar contains five white, three black, and two green stones. What is the probability of drawing a black stone on a single draw?

The word R A N D O M has been spelled in a game of Scrabble. If two letters are chosen from this word at random, what is the probability that they are both consonants?

The names of all 30 party guests are placed in a box, and one name is drawn to award a door prize. If you and your date are among the guests, what is the probability that one of you will win the prize?

If two people are chosen at random from a group consisting of five men and three women, what is the probability that one man and one woman are chosen?

A company determines that 32% of the e-mail it receives is junk mail. What is the probability that a randomly chosen e-mail at this company is not junk mail?

If 2 cards are drawn from a standard 52-card deck, what is the probability that both are clubs?

A battery manufacturer inspects 500 batteries and finds that 30 are defective. What is the probability that a randomly selected battery is not defective?

A ball is taken at random from a pool table containing balls numbered 1 through 9. What is the probability of obtaining (a) ball number 7? (b) an even-numbered ball? (c) an odd-numbered ball?

A clothes dryer load contains two shirts, four pairs of socks, and three nightgowns. You pull one item randomly from the dryer.

1. What is the probability that it is a sock?

2. What is the probability that it is a nightgown?