## 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:     AN = A1 + D (N - 1)   where:     A1 is the first term,     AN 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:     A20 = 2 + 2 x (19) = 2 + 38 = 40 The formula for the sum of the first N terms of an arithmetic sequence is:     Sum = (A1 + AN) N / 2 where:     A1 is the first element of the sequence     AN 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