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Lesson · Grade 10 · Foundations of Mathematics and Pre Calculus

Arithmetic sequences: first term and common difference

  • Grade 10
  • Foundations of Mathematics and Pre Calculus
  • 2 min 4 s
  • British Columbia
  • BC10-MA-20

Using 7, 11, 15, 19, ... the video names the first term (7), subtracts each term from the next to find the common difference (4), and checks the next term: 19 + 4 = 23. It then shows that 50, 47, 44, ... is a decreasing sequence with common difference −3, where subtracting the wrong way gives the wrong sign, and that 2, 4, 8, 16 is not arithmetic because each term doubles.

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In one sentence

The question this lesson answers

Here is a sequence: 7, 11, 15, 19, and so on. What makes it an arithmetic sequence?

A sequence is a list of numbers in order. Each number in it is called a term.

Transcript

What the lesson says

Here is a sequence: 7, 11, 15, 19, and so on. What makes it an arithmetic sequence?

A sequence is a list of numbers in order. Each number in it is called a term.

The first term is the one the sequence starts with. Here, it is 7.

Now subtract each term from the next one.

11 minus 7 is 4. 15 minus 11 is 4. 19 minus 15 is 4.

The difference is the same each time. It is called the common difference, and here it is 4.

A sequence with a common difference, like this one, is called an arithmetic sequence.

To get the next term, add 4: 19 plus 4 is 23.

Now look at 50, 47, 44, and so on.

47 minus 50 is negative 3. 44 minus 47 is negative 3.

The common difference is negative 3. Each term is 3 less than the one before, so the sequence is decreasing.

A common mistake is to subtract the other way round: 50 minus 47 is 3, which has the wrong sign.

Always take the next term minus the term before it.

Now try 2, 4, 8, 16.

4 minus 2 is 2. 8 minus 4 is 4. 16 minus 8 is 8.

The differences change, so this sequence is not arithmetic. Each term is double the one before.

To recap: an arithmetic sequence starts at its first term, here 7, and adds the same common difference, here 4, every time.

Curriculum

Where this fits

British Columbia, Grade 10

Foundations of Mathematics and Pre Calculus 10, Linear relations: arithmetic sequencesBC10-MA-20

Previous: Writing the equation of a line from a table of valuesNext: The General Term of an Arithmetic Sequence

The outcomes and strands follow the British Columbia curriculum.

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