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Let S_k denote the sum of first k terms of an AP. What is S₃₀ S₂₀-S₁₀ equal to?

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

C. 3

Step-by-step solution

Let first term be ' a ' and common differenced be ' d ' of an A.P. aligned & s₃₀ s₂₀-s₁₀ = 30 2 [2 a+29 d] 20 2 [2 a+19 d]- 10 2 [2 a+9 d] & = 15[2 a+29 d] 20 a+190 d-10 a-45 d & = 15(2 a+29 d) 10 a+145 d = 15(2 a+29 d) 5(2 a+29 d) =3 aligned

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