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Section 1 · Explained simply
What is an Arithmetic Progression?
An Arithmetic Progression (AP) is a list of numbers where you add the same fixed amount each time to get the next number. That fixed amount is called the common difference, written as d.
Worked example
2, 5, 8, 11, 14, … Start = 2, and each time we add 3. So d = 3.
The nth term formula
aₙ = a + (n − 1)d
a = first term · n = position · d = common difference.
To find the 10th term of 2, 5, 8…: a = 2, d = 3, n = 10 → aₙ = 2 + (10−1)×3 = 29.
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Curiosity · Section 4
Why is the area of a rectangle l × b, not l + b?
Because area measures how many unit squares fit inside — and multiplying counts them, adding doesn't.
See it visually
A 5 × 3 rectangle = length (5) added breadth-times (3) = 15 squares. That's exactly what l × b means.
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Watch: the intuition in 90 sec
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Think like a topper
The 3 questions that build real understanding
1
WHY
An AP grows by a fixed step, so the nth term is just the start plus that step taken (n−1) times. The formula is a shortcut for counting steps, not a rule to memorise.
2
WHAT IF
What if d = 0? Every term is the same — still a valid AP.
What if n comes out a decimal? The term simply isn't in the sequence.
What if the terms decrease? Then d is negative — the maths still holds.
3
NOW WHAT
When an answer looks weird in an exam, pause and ask: is this possible, and why? A negative number of terms or a decimal position is a signal to re-check — not to panic.
📖 The two students' story
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Two students solve the same AP problem and both get n = −4. One writes it down and moves on. The other pauses: "You can't have a negative number of terms." She spots her sign error, fixes it, and gets it right. Same knowledge — different habit of mind.
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Practice · Q3 of 6
Medium
Find the 15th term of the AP: 3, 7, 11, 15, …
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✓ Correct! Step-by-step:
a = 3, d = 4, n = 15 → aₙ = 3 + (15−1)×4 = 3 + 56 = 59
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Question 5 / 10
⏱ 04:12
Which term of the AP 5, 8, 11, … is equal to 47?
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Concept mastery
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📌 Revise: nth-term with negative d
You missed 2 questions on decreasing APs.
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Arithmetic Progression
Section 3 · Practice Questions
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Ask AI Tutor
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I don't get why d can be negative.
Great question! d is just the step between terms. If the numbers go down — like 20, 17, 14 — you're subtracting 3 each time, so the step is −3. Same rule, negative direction. 👍
💡 Want me to show 20, 17, 14 on a number line?
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Aarav Mehta
Class 10 · Holy Bless School
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