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Common difference

The common difference is the fixed number added to each term of an AP to get the next term.

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Student-friendly explanation

If you subtract any term from the next term in an AP, you get the same value every time. That value is the common difference, written as d. It can be positive, negative, or zero. This is one of the most important ideas in the chapter because almost every AP formula uses d.

How to write this in exams

  1. 1

    Start with the exact idea

    The common difference is the fixed number added to each term of an AP to get the next term.

  2. 2

    Then show how to use it

    1. Take two consecutive terms. 2. Subtract the first from the next term. 3. Check another pair to confirm. 4. Keep the sign as it appears from the sequence order.

  3. 3

    Add one concrete example

    In 15, 11, 7, 3, ... the common difference is -4 because each term is 4 less than the previous term.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is to use the absolute difference without sign. That hides whether the AP is increasing or decreasing.

Definition

The common difference is the fixed number added to each term of an AP to get the next term.

Example

In 15, 11, 7, 3, ... the common difference is -4 because each term is 4 less than the previous term.

Rule to remember

For an AP, d = a2 - a1 = a3 - a2 = a4 - a3 and so on.

Memory hook

d means the same step repeats every time.

Examples and method

Worked example

For 3, 8, 13, 18, ... we get d = 8 - 3 = 5, and checking again gives 13 - 8 = 5. So the common difference is 5.

Method to apply

1. Take two consecutive terms. 2. Subtract the first from the next term. 3. Check another pair to confirm. 4. Keep the sign as it appears from the sequence order.

Diagram support

A number line or list with arrows between consecutive terms helps students see the repeated change.

How CBSE asks it

Questions may ask students to find d from a sequence, identify a mistake in sign, or use d in a formula.

Avoid common mistakes

Common confusion

Students often write the difference as a larger number minus a smaller number in the wrong order, which changes the sign.

Common wrong answer

A common wrong answer is to use the absolute difference without sign. That hides whether the AP is increasing or decreasing.

Exam tip

Keep the order of subtraction the same as the order of the sequence: next term minus previous term.

Quick check

What does the common difference tell you in an AP?

The common difference tells you the fixed number added to or subtracted from each term to get the next term. It shows the regular step size of the sequence.

Answer writing and exam use

1-mark answer

The common difference is the fixed number added to each term of an AP to get the next term.

2-mark answer

The common difference is the fixed number added to each term of an AP to get the next term. For an AP, d = a2 - a1 = a3 - a2 = a4 - a3 and so on. In 15, 11, 7, 3, ... the common difference is -4 because each term is 4 less than the previous term.

3-mark answer

If you subtract any term from the next term in an AP, you get the same value every time. That value is the common difference, written as d. It can be positive, negative, or zero. This is one of the most important ideas in the chapter because almost every AP formula uses d. For an AP, d = a2 - a1 = a3 - a2 = a4 - a3 and so on. For 3, 8, 13, 18, ... we get d = 8 - 3 = 5, and checking again gives 13 - 8 = 5. So the common difference is 5. Questions may ask students to find d from a sequence, identify a mistake in sign, or use d in a formula. A common wrong answer is to use the absolute difference without sign. That hides whether the AP is increasing or decreasing.
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