- A160
- B80
- C72
- D88
Step-by-Step Solution
Angles in AP sum to 180. Middle angle = 180/3 = 60. So angles are 40, 60, 80. Largest = 80 degrees.
Answer: B) 80
The angles of a triangle are in AP. If the smallest angle is 40 degrees, find the largest angle in degrees.
Class 10Arithmetic ProgressionsAlgebra — Sequences
Key idea: n-th term formula
**aₙ = a + (n − 1)d**
Where a is the first term, d is the common difference, n is the position.
**Why**: a₁ = a; a₂ = a + d; a₃ = a + 2d; … aₙ = a + (n − 1)d. Each step adds another d.
**Example**: AP 3, 7, 11, 15, …. Find the 20th term.
a = 3, d = 4. a₂₀ = 3 + 19·4 = 79.
**Reverse use**: 'In the AP 5, 11, 17, …, which term is 89?' a + (n−1)d = 89 → 5 + 6(n−1) = 89 → n = 15.
Where a is the first term, d is the common difference, n is the position.
**Why**: a₁ = a; a₂ = a + d; a₃ = a + 2d; … aₙ = a + (n − 1)d. Each step adds another d.
**Example**: AP 3, 7, 11, 15, …. Find the 20th term.
a = 3, d = 4. a₂₀ = 3 + 19·4 = 79.
**Reverse use**: 'In the AP 5, 11, 17, …, which term is 89?' a + (n−1)d = 89 → 5 + 6(n−1) = 89 → n = 15.
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