Single correct option
The sum of the first n terms of an arithmetic progression is 2n² + 7n. What is its 20th term?
- A. 85
- B. 90
- C. 80
- D. 95
Show answer and solution
Answer: (A) 85
The nth term is Tₙ = Sₙ − Sₙ₋₁.
Sₙ − Sₙ₋₁ = 2n² + 7n − [2(n − 1)² + 7(n − 1)] = 2(2n − 1) + 7 = 4n + 5.
T₂₀ = 4 × 20 + 5 = 85.
Check: T₁ = S₁ = 9 = 4 + 5 ✓.
Tip: If Sₙ = an² + bn, then Tₙ = 2an + (b − a) and the common difference is 2a.
Sₙ − Sₙ₋₁ = 2n² + 7n − [2(n − 1)² + 7(n − 1)] = 2(2n − 1) + 7 = 4n + 5.
T₂₀ = 4 × 20 + 5 = 85.
Check: T₁ = S₁ = 9 = 4 + 5 ✓.
Tip: If Sₙ = an² + bn, then Tₙ = 2an + (b − a) and the common difference is 2a.
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