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Common Difference
d = a2-a1 = a3-a2. If the differences are not equal, it is not an AP. 3, 3, 3, ... is an AP with d=0.
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Common Difference
What is it?
d = a2-a1 = a3-a2. If the differences are not equal, it is not an AP. 3, 3, 3, ... is an AP with d=0.
In simple words
- d = a2-a1 = a3-a2.
- 5,9,13 d=4
- 10,7,4 d=-3
- State the rule, show the working, and check the answer.
Important terms
COMMON DIFFERENCE: d = a2-a1 = a3-a2. If the differences are not equal, it is not an AP. 3, 3, 3, ... is an AP with d=0.
COMMON DIFFERENCE: d = a2-a1 = a3-a2.
What you should learn
- State the rule or meaning of common difference in easy words.
- Apply common difference in a clear step-by-step solution.
- Check the conditions, working, and final answer for accuracy.
Examples
- 5,9,13 d=4
- 10,7,4 d=-3
- Not 1,2,4,8
MAIN IDEA
d = a2-a1 = a3-a2. If the differences are not equal, it is not an AP. 3, 3, 3, ... is an AP with d=0.
EXAM USE
Write the rule first: d = a2-a1 = a3-a2. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Recommended for Class 11
Full school-level explanation
d = a2-a1 = a3-a2. If the differences are not equal, it is not an AP. 3, 3, 3, ... is an AP with d=0.
Understand the idea, then apply it:
WHAT — COMMON DIFFERENCE
d = a2-a1 = a3-a2. If the differences are not equal, it is not an AP. 3, 3, 3, ... is an AP with d=0.
WHY — Why it matters
This rule is a separate learning unit inside arithmetic sequence. It can be defined, applied, and checked in its own FBISE question.
HOW — How to answer
Write the rule first: d = a2-a1 = a3-a2. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
MAIN IDEA
d = a2-a1 = a3-a2. If the differences are not equal, it is not an AP. 3, 3, 3, ... is an AP with d=0.
Remember
- subtract neighbours
Examples
- 5,9,13 d=4
- 10,7,4 d=-3
- Not 1,2,4,8
EXAM USE
Write the rule first: d = a2-a1 = a3-a2. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Remember
- focused answer
- accurate support
Examples
- State the central idea
- Use one accurate detail
- Check the final response
How to answer a common difference question
How it works
- Read the exact command word and identify what the question asks.
- State the matching idea, rule, or meaning before adding detail.
- Use the unit evidence or mathematical working that directly supports the answer.
- Check accuracy, relevance, and answer length before finishing.
Remember
- subtract neighbours
- common difference d
- an = a + (n-1)d
- n-1 jumps
- subtract neighbours
- focused answer
- accurate support
- subtract neighbours
Deeper understanding
Go beyond memorising Common Difference. Connect the definition to reasons, relationships, exceptions, and exam wording.
Common mistakes
Exam focus
Core Idea
What to Know
Example or Evidence
How to Answer
Exam focus
Quick revision
- subtract neighbours
- common difference d
- an = a + (n-1)d
- n-1 jumps
- COMMON DIFFERENCE: d = a2-a1 = a3-a2. If the differences are not equal, it is not an AP. 3, 3, 3, ... is an AP with d=0
- COMMON DIFFERENCE: d = a2-a1 = a3-a2.
The jump is (n-1) steps from a1, not n steps. 7th term uses 6 jumps.
For long answers on Common Difference: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- subtract neighbours
- common difference d
- an = a + (n-1)d
- n-1 jumps
Important formulas
- subtract neighbours
- common difference d
- an = a + (n-1)d
Common exam traps
- The jump is (n-1) steps from a1, not n steps. 7th term uses 6 jumps.
- Do not choose a formula before checking that its conditions fit the question.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
The jump is (n-1) steps from a1, not n steps. 7th term uses 6 jumps.
- Mistake
Do not choose a formula before checking that its conditions fit the question.
- Mistake
Do not hide sign changes, restrictions, or skipped algebra steps.
- Mistake
The jump is (n-1) steps from a1, not n steps. 7th term uses 6 jumps.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
subtract neighbours
common difference d
an = a + (n-1)d
n-1 jumps
d = a2-a1 = a3-a2. If the differences are not equal, it is not an AP. 3, 3, 3, ... is an AP with d=0.
an = a + (n-1)d
- Definition
- d = a2-a1 = a3-a2. If the differences are not equal, it is not an AP. 3, 3, 3, ... is an AP with d=0.
- Formula
- an = a + (n-1)d
- Example
- 5,9,13 d=4
- Critical warning
- The jump is (n-1) steps from a1, not n steps. 7th term uses 6 jumps.
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Exam Practice
Define
Q1. Define Common Difference.
Explain
Q2. Explain: MAIN IDEA.
Example
Q3. Give one clear example of Common Difference and say why it fits.
Mistake
Q4. State one common mistake students make about Common Difference.
Exam note
Q5. Write a short exam note on Common Difference: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.