Single correct option
The sum of the first n terms of an arithmetic progression is 3n² + 5n. What is its 15th term?
- A. 92
- B. 88
- C. 95
- D. 98
Show answer and solution
Answer: (A) 92
T₁₅ = S₁₅ − S₁₄ = (3·225 + 75) − (3·196 + 70) = 750 − 658 = 92.
General term: Tₙ = Sₙ − Sₙ₋₁ = 6n + 2, so T₁₅ = 92 ✓ (first term 8, common difference 6).
Tip: If Sₙ = an² + bn, the common difference is 2a and the first term is a + b.
General term: Tₙ = Sₙ − Sₙ₋₁ = 6n + 2, so T₁₅ = 92 ✓ (first term 8, common difference 6).
Tip: If Sₙ = an² + bn, the common difference is 2a and the first term is a + b.
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