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What is a Sequence?

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

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Student-friendly explanation

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.

How to write this in exams

  1. 1

    Start with the exact idea

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

  2. 2

    Then show how to use it

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

  3. 3

    Add one concrete example

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

  4. 4

    Avoid this incomplete 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.

Definition

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

Example

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

Rule to remember

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

Memory hook

Sequence means order first, pattern next.

Examples and method

Worked example

For 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. The pattern is adding 3 each time.

Method to apply

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

Diagram support

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

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.

Avoid common mistakes

Common confusion

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.

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.

Exam tip

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

Quick check

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

The third term is 15 because it is the number written in the third position of the ordered list.

Answer writing and exam use

1-mark answer

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

2-mark answer

A sequence is an ordered list of numbers, objects, or quantities written according to a rule or pattern. A sequence is commonly written as a1, a2, a3, ..., an, where an means the term in the nth position. In 4, 7, 10, 13, the first term is 4, the second term is 7, and each next term increases by 3.

3-mark answer

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. A sequence is commonly written as a1, a2, a3, ..., an, where an means the term in the nth position. For 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. The pattern is adding 3 each time. 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. 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.
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