Page 1: Introduction
Arithmetic Progression (AP): sequence where each term after first is obtained by adding constant difference to previous term.
Constant difference = common difference (d).
Example: 2, 5, 8, 11,... (d=3)
Page 2: General Form of AP
a, a+d, a+d+d, ... or a, a+d, a+2d, ...
a = first term
d = common difference
If d > 0 → increasing AP
d < 0 → decreasing AP
d = 0 → constant sequence
Page 3: nth Term of AP
n = term number
Most important formula.
Page 4: Sum of First n Terms
or S_n = n/2 (a + l) (l = last term)
Derived from pairing terms.
Page 5: Properties of AP
- If same term added/subtracted → still AP
- If multiplied/divided by non-zero constant → still AP
- Three terms a-d, a, a+d → symmetric
Page 6: Selecting Terms in AP
For 3 terms: a-d, a, a+d
For 4 terms: a-3d, a-d, a+d, a+3d
For 5 terms: a-2d, a-d, a, a+d, a+2d
Page 7: Word Problems
Form AP from statement → use a_n or S_n.
Common: savings, salary, seats, wages.
Page 8: Key Formulas Summary
S_n = n/2 [2a + (n-1)d]
S_n = n/2 (a + l)
Page 9: Practice Questions - Easy (1-10)
- Common difference of 3,7,11,15.
- 10th term of AP 5,10,15...
- Sum of first 20 terms a=2, d=3.
- Is 1,1,1,1 AP?
- nth term formula.
- Three terms in AP with middle 10, common difference 4.
- Last term l = a + ?
- S_n formula with l.
- Number of terms if a_n given.
- d from a_5 = 20, a_10 = 35.
Page 10: Practice Questions - Medium (11-20)
- Find n if S_n = 225, a=5, d=4.
- 20th term from end in AP with 30 terms.
- Sum of AP with a=7, l=55, n=25.
- Which term of AP 20,18,16... is 0.
- Find a and d if a_4=10, a_8=22.
- Sum of first 100 natural numbers.
- Three numbers in AP sum 24, product 440.
- Monthly salary starts 20000, increases 2000, find after 2 years.
- Seats in rows AP, find total seats.
- Find k if k-1, k, k+1 in AP.
Page 11: Practice Questions - Hard (21-30)
- Sum of n terms where terms in AP.
- Find number of terms in savings problem.
- AP with common difference fraction.
- Prove sum formula derivation.
- Advanced word problem with multiple AP.
- Find three terms given sum and sum of squares.
- Salary increase problem with total amount.
- Board level numerical.
- Terms from end calculation.
- Find a, d, n from given data.
Page 12: Important Formulas Table
nth term, sum, last term.
Page 13: Common Mistakes
- Wrong (n-1)d in a_n
- Forgetting n/2 in sum
- Mixing a and l
- Wrong term from end
- Sign error in negative d
Page 14: Previous Year Questions
nth term, sum, word problems, find n/k.
Page 15: Exam Tips
- Memorise both sum formulas
- Identify a and d correctly
- Show steps in word problems
- Use S_n = n/2 (a+l) when l given
- Practice term from end
Page 16: Quick Revision Sheet
All formulas, properties, examples.
Page 17: Final Motivation
Chapter 5 complete! AP is easy and scoring.
Master word problems.
Class 10 Maths unstoppable 🦖
Page 18: Extra Numericals
More solved problems.
Page 19: Word Problem Types
Savings, salary, seats, numbers.
Page 20: Sum Formula Derivation
Pairing method.
Page 21: Term from End
Formula and method.
Page 22: Board Pattern Questions
Common types.
Page 23: Extra Practice
More questions.
Page 24: Properties of AP
Detailed examples.
Page 25: Real-Life Applications
Interest, growth, arrangements.
Page 26: Selecting Terms
3,4,5 terms in AP.
Page 27: Thank You & Copyright
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