Arithmetic sequence
An arithmetic sequence is a sequence of numbers in which the same number is added or
subtracted from each element to get the next number in the sequence. Here are some arithmetic sequences:
2, 4, 6, 8, 10, ... 
2 is added to each term to get the next term in the sequence

11, 8, 5, 2, 1, 4 ... 
3 is added to each term to get the next term in the sequence. You can also think of this as 3 being subtracted from each term to get the next one 
Here's a question for you: What is the next number in this arithmetic sequence?
1 4 7 10 ___
Here are some common arithmetic sequence problems:
Find the Nth term of an arithmetic sequence  Find the sum of the first N terms of an arithmetic sequence: 
The formula for computing the Nth term in an arithmetic sequence is:
A_{N} = A_{1} + D (N  1)
where:
A_{1} is the first term,
A_{N} is the Nth term (the term you are looking for)
D is the number that is added to each term.
So, the 20th term of the first sequence above
(2, 4, 6, . . .) is:
A_{20} = 2 + 2 x (19) = 2 + 38 = 40

The formula for the sum of the first N terms of an arithmetic sequence is:
Sum = (A_{1} + A_{N}) N / 2 where:
A_{1} is the first element of the sequence
A_{N} is the Nth element of the sequence
So, the sum of the first 20 odd integers is:
Sum = (1 + 39) X 20 /2 = 40 X 10 = 400

Here are 2 questions for you:
1. What is the 40th term of the sequence 2, 4, 6, 8, 10, ...? _____
2. What is the sum of the first 40 terms of that sequence? ______
Hint: You need the answer to question 1 to answer question 2
