All about Arithmetic Sequence

Study Notes

The common difference of the arithmetic sequence 5, 11, 17, 23,... is 6.
The 10th term of the arithmetic sequence 2, 7, 12, 17,... is 47.
Given an arithmetic sequence with a first term of 3 and a common difference of 4, the 8th term is 31.
Given that the 5th term of an arithmetic sequence is 22 and the 10th term is 47, the first term is 2.
The sum of the first 15 terms of an arithmetic sequence with a first term of 1 and a common difference of 3 is 345.
Given that the sum of the first 20 terms of an arithmetic sequence is 950 and the common difference is 4, the first term is 2.
Three arithmetic means inserted between 5 and 29 are 11, 17, and 23.
Given that the sum of the first and last term of an arithmetic sequence is 42 and there are 10 terms in the sequence, the sum of all the terms is 210.
In an arithmetic sequence where the 12th term is 52 and the 17th term is 77, the common difference is 5.
Given an arithmetic sequence where the sum of the first and third term is 12 and the fifth term is 16, the first term is 2.

There are 120 (5!) ways to arrange 5 people in a line.
There are 120 (10C3) ways to select 3 books from a shelf of 10 books.
Given a bag containing 5 red marbles and 3 blue marbles, the probability of drawing a red marble is 5/8.
The probability of getting two heads when a coin is tossed twice is 1/4.
The probability of getting an even number when a die is rolled is 1/2.
There are 24 (4!) different ways to arrange the letters in the word "MATH".
There are 56 (8C3) different committees that can be formed when a committee of 3 people is selected from a group of 8 people.
The probability of drawing two aces from a standard deck of 52 cards without replacement is 1/221.
Given a box containing 5 red balls, 3 blue balls, and 2 green balls, the probability of drawing a blue ball is 3/10.
A pizza parlor offering 3 types of crusts and 5 different toppings can make 15 (3 crusts * 5 toppings) different one-topping pizzas.