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medium difficulty6 min

What is a Sequence?

A sequence is an ordered list of numbers, objects, or quantities written according to a rule or pattern.

In one line: Sequence means order first, pattern next.

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Understand it

In a sequence, the position of a term matters. The first term, second term, third term, and so on are not just values; they are values attached to places. For example, 3, 6, 9, 12 is different from 12, 9, 6, 3 because the order has changed.

Example

In 4, 7, 10, 13, the first term is 4, the second term is 7, and each next term increases by 3.

Formula and rule

A sequence is commonly written as a1, a2, a3, ..., an, where an means the term in the nth position.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

  1. 1For the sequence 2, 5, 8, 11, the term in position 1 is 2, position 2 is 5, position 3 is 8, and position 4 is 11.
  2. 2The pattern is adding 3 each time.

Method you can reuse

  1. 1Read the terms in order.
  2. 2Mark their positions.
  3. 3Compare consecutive terms.
  4. 4State the pattern.
  5. 5Use the pattern only after checking at least two steps.

Visual tip

A simple row diagram with boxes labelled position 1, position 2, position 3 can help show that each term has a fixed place.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

In the sequence 5, 10, 15, 20, what is the third term and why?

Think first, then show answer
The third term is 15 because it is the number written in the third position of the ordered list.

Common wrong answer

For 2, 5, 8, 11, some students write 12 as the next term by adding 1 to the last digit pattern, but the correct next term is 14 because the sequence increases by 3.

Don't mix this up

Students often look only at the numbers and ignore their positions, so they may reverse the sequence or choose a term without checking its place.

Exam tip

Always write the term position along with the term value when solving missing-term or nth-term questions.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Students may be given a list such as 6, 11, 16, 21 and asked to find the next term, identify a particular term, or describe the pattern.
  1. 1

    Enough for 1 mark

    A sequence is an ordered list of numbers, objects, or quantities written according to a rule or pattern.

  2. 2

    Add for 2 marks

    Example: In 4, 7, 10, 13, the first term is 4, the second term is 7, and each next term increases by 3.

  3. 3

    Add for 3 marks

    In a sequence, the position of a term matters.

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