MathematicsChapter 4: Sequences and Series
Common Difference
d = a2-a1 = a3-a2. If the differences are not equal, it is not an AP.
Learning objectives
- 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.
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.
Mathematical form
d = a2-a1
d=0.
Where / symbols
- 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.
Relationship
- an = a + (n-1)d
Overview
Understand the idea, then apply it:
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.
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.
Examples State the central idea · Use one accurate detail · Check the final response
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.
How to answer a common difference question
- 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.
In simple words
The jump is (n-1) steps from a1, not n steps. 7th term uses 6 jumps.
Key points
- subtract neighbours
- common difference d
- an = a + (n-1)d
- focused answer
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Common Difference
Sticky Notes · Quick Revision
Core Idea
- d = a2-a1 = a3-a2.
What to Know
- 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.
Example or Evidence
- 5,9,13 d=4
- 10,7,4 d=-3
- Not 1,2,4,8
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.
Common Error
- The jump is (n-1) steps from a1, not n steps. 7th term uses 6 jumps.
FBISE Exam Check
- State the rule, show the working, and check the answer.
60-second revision
- 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.
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