Key Concepts
- 1nth term of AP
- 2Sum of n terms (form 1)
- 3Sum of n terms (form 2)
- 4Sum of first n natural numbers
- 5Finding d from two terms
- 6Finding aₙ from Sₙ
- 7Arithmetic mean
- 8Three numbers in AP
- 9nth term of AP
- 10Sum of n terms (form 1)
Important Formulas & Facts
#1
aₙ = a + (n-1)d
#2
Sₙ = n/2 [2a + (n-1)d]
#3
Sₙ = n/2 [a + l] where l = last term
#4
n(n+1)/2
#5
d = (aₘ - aₙ)/(m - n)
#6
aₙ = Sₙ - Sₙ₋₁ (for n ≥ 2)
#7
AM of a and b = (a + b)/2
#8
Take them as a-d, a, a+d
#9
aₙ = a + (n-1)d
#10
Sₙ = n/2 [2a + (n-1)d]
Must-Know Questions
Q1Find the 10th term of AP: 2, 7, 12, 17, ...
Explanation
a = 2, d = 5. a₁₀ = a + 9d = 2 + 45 = 47.
Q2Find the sum of first 20 terms of AP: 1, 4, 7, 10, ...
Explanation
a = 1, d = 3, n = 20. S₂₀ = 20/2 × [2(1) + 19(3)] = 10 × [2 + 57] = 590.
Q3Which term of AP 3, 8, 13, 18, ... is 78?
Explanation
a = 3, d = 5. aₙ = 3 + (n-1)5 = 78. (n-1)5 = 75. n = 16.
Q4If the 3rd and 9th terms of an AP are 4 and -8, find the common difference.
Explanation
a₃ = a + 2d = 4, a₉ = a + 8d = -8. Subtract: 6d = -12, d = -2.
Q5Find the sum of first 100 natural numbers.
Explanation
S = n(n+1)/2 = 100 × 101/2 = 5050.
Practice Arithmetic Progressions
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