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
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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
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