- A3
- B2
- C4
- D1
Step-by-Step Solution
→ → . Also a₇ = ₃ + 1: → → . Substitute → → .
Answer: B) 2
The 4th term of an AP is equal to 3 times its first term, and the 7th term exceeds twice the 3rd term by 1. Find the common difference.
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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