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Let S_n= 1 2 + 1 6 + 1 12 + 1 20 + upto n terms. If the sum of the first six terms of an A.P. with first term -p and common difference p is 2026 ~S ₂₀₂₅ , then the absolute difference betwen 20^ th and 15^ th terms of the A.P. is

Options

  1. A20
  2. B90
  3. C45
  4. D25

Correct answer

D. 25

Step-by-step solution

aligned & Sn = 1 2 + 1 6 + 1 12 + 1 20 . N terms & S ₂₀₂₅= _ n =1 ²⁰²⁵ 1 n ( n +1) = _ n =1 ²⁰²⁵ ( 1 n - 1 n +1 ) & = ( 1 1 - 1 2 )+ ( 1 2 - 1 3 ) ( 1 2025 - 1 2026 ) aligned aligned & = 2025 2026 & 2026 . S ₂₀₂₅ = 2025 =45 aligned Given : 6 2 [-2 p+(6-1) p]=45 aligned & 9 p =45 & p =5 & | ~A ₂₀- A ₁₅ |=|-5+19 5|-[-5+14 5] & =|90-65| & =25 aligned

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