Single correct option
A sequence is defined by a₁ = 1 and aₙ₊₁ = aₙ + 2n for n ≥ 1. What is a₂₀?
- A. 361
- B. 380
- C. 381
- D. 401
Show answer and solution
Answer: (C) 381
Unrolling the recurrence: a₂₀ = a₁ + 2(1 + 2 + … + 19) = 1 + 2 × 190 = 381.
In general aₙ = 1 + n(n − 1), e.g. a₂ = 3, a₃ = 7 ✓.
380 forgets a₁; 401 sums up to 20 instead of 19 (1 + 2 × 200). Watch the upper limit: going from a₁ to a₂₀ takes 19 steps.
In general aₙ = 1 + n(n − 1), e.g. a₂ = 3, a₃ = 7 ✓.
380 forgets a₁; 401 sums up to 20 instead of 19 (1 + 2 × 200). Watch the upper limit: going from a₁ to a₂₀ takes 19 steps.
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