Single correct option
The sum of the first n terms of an arithmetic progression is 3n² + 5n for every n. Which term of the progression is 152?
- A. 24th
- B. 25th
- C. 26th
- D. 27th
Show answer and solution
Answer: (B) 25th
Tₙ = Sₙ − Sₙ₋₁ = (3n² + 5n) − [3(n − 1)² + 5(n − 1)] = 6n + 2.
(Check: T₁ = S₁ = 8 = 6 + 2 ✓.)
6n + 2 = 152 ⇒ n = 25. So 152 is the 25th term.
Tip: when Sₙ = An² + Bn, the common difference is 2A (here 6) and T₁ = A + B (here 8).
(Check: T₁ = S₁ = 8 = 6 + 2 ✓.)
6n + 2 = 152 ⇒ n = 25. So 152 is the 25th term.
Tip: when Sₙ = An² + Bn, the common difference is 2A (here 6) and T₁ = A + B (here 8).
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