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If the sum of 12 th and 22 nd terms of an AP is 100 , then the sum of the first 33 terms of an AP is

Options

  1. A1700
  2. B1650
  3. C3300
  4. D3500

Correct answer

B. 1650

Step-by-step solution

Here, T₁₂=a+11 d and T₂₂=a+21 d Since, 100=T₁₂+T₂₂ aligned & 100=a+11 d+a+21 d & a+16 d=50 ( i ) aligned Now, aligned S₃₃ & = 33 2 [2 a+(33-1) d] & =33(a+16 d)=33 50 [From Eq. (i)] & 1650 aligned Thus, required sum be 1650 .

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