These are sequences where the difference from one term to the next remains constant, like the one in the title! Arithmetic sequences crop up in all sorts of places and this unit looks at understanding how to generalise, sum and solve problems involving arithmetic sequences.
Key Concepts
In this unit you should learn to…
recognise arithmetic sequences
find the nth term of an arithmetic sequence
find missing terms in an arithmetic sequence
find the sum of an arithmetic sequence
Essentials
Slides Gallery
Use these slides to review the material and key points covered in the videos.
1. What is an Arithmetic Sequence
This video describes the nature and properties of an arithmetic sequence.
2. Finding the nth term of an arithmetic sequence
This video goes over the process of describing arithmetic sequences generally.
3. Finding terms of an arithmetic sequence
How to find terms with a given position in the sequence. For example, for a given sequence, how do you find the 15th term?
4. Sigma Notation
This video describes what sigma notation is. There are additional videos on the TI-84, Ti-Nspire and Casio pages which show you how to evaluate a series in sigma notation on the GDC.
5. Finding the sum of an arithmetic sequence
How do we find the total of a given number of terms of an arithmetic sequence?
Summary
This section of the page can be used for quick review. The flashcards help you go over key points and the quiz lets you practice answering questions on this subtopic.
Flash Cards
Review these condensed 'key point' flashcards to help you check and keep ideas fresh in your mind.
Test Yourself
Self Checking Quiz
Practice your understanding on these quiz questions. Check your answers when you are done and read the hints where you got stuck. If you find there are still some gaps in your understanding then go back to the videos and slides above.
1
Which of the following sequences could be arithmetic
Arithmetic sequences must have a constant difference between the terms. Four of the answers do not. The others could be arithmetic sequences because they do.
2
What is the common difference in this sequence? 2, 1.8, 1.6, 1.4 (no spaces in your answer)
Sequence goes down by 0.2 each time so the difference is -0.2
3
The general term of an arithmetic sequence is given by Un = 3 + 4(n - 1), what is the 10th term of this sequence?
Substitute n = 9 into the nth term and get U10 = 3 + 4 X 9, so U10 = 39
4
Consider the following sequence, Un = -2 + 0.5(n - 1), work out the 8th and 15th terms and add them together.
Substitute n = 8 and 15 in to the general term. The 8th term is 1.5, 15th term is 5, together they sum to 6.5
5
An arithmetic sequence begins 5, 14, 23, 32..... Which of the following is the nth term of that sequence
Using the formula for the nth term, Un = U1 + d(n - 1), substitue U1 = 5 and d = 9
6
Consider the arithmetic sequence that begins 15, 31, 47.... Calculate the sum of the the first ten terms of this sequence.
Substitue U1 = 15 and d = 16 in to the sum formula, or work out that U10 = 159 and use the other formula
7
Calculate the sum of the first 20 terms of this sequence Un = 10 - 4(n - 1)
Substitue U1 = 10 and d = -4 in to the sum formula, or work out that U20 = -66 and use the other formula
8
An arithmetic sequence has U4 = 18 and U7 = 30, what is the first term of the sequence?
Work out that the common difference ias added 3 times between the 4th and 7th term and this is +12 all together so d = 4. Subtract the value of d 3 times to get back to the first term.
9
An arithmetic sequence has U2 = 18 and U9 = 53, what is the 10th term of the sequence?
Work out that the common difference ias added 7 times between the 2nd and 9th term and this is +35 all together so d = 5. Add the value of d once to get from the 9th to 10th terms.
10
Which is greater,
a) The sum of the sequence Un = 150 + 25(n - 1) to the first 20 terms or
b) The sum of the sequence Un = 150 + 20(n - 1) to the first 25 terms
The first sum is 7750 and the second is 9750
Exam Style Questions
The following questions are based on IB exam style questions from past exams. You should print these off (from the document at the top) and try to do these questions under exam conditions. Then you can check your work with the video solution.
Question 1
Video solution
Question 2
Video solution
Question 3
Video solution
MY PROGRESS
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