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Arithmetic Progressions · Class 10 · CBSE Mathematics

Find the sum of the first 22 terms of the AP: 8, 3, -2, dots.

Practice question from Arithmetic Progressions (Class 10 · CBSE Mathematics), with the correct answer and a step-by-step solution.

medium · MCQ · Q-2C4339

Find the sum of the first 22 terms of the AP: 8,3,−2,…8, 3, -2, \dots.

  1. A.-979Correct answer
  2. B.-611
  3. C.611
  4. D.979

Solution

Here a=8a = 8, d=3−8=−5d = 3 - 8 = -5, and n=22n = 22. Using the sum formula Sn=n2[2a+(n−1)d]S_n = \frac{n}{2}[2a + (n-1)d], we get S22=222[2(8)+(22−1)(−5)]=11[16+21(−5)]=11[16−105]=11[−89]=−979S_{22} = \frac{22}{2}[2(8) + (22-1)(-5)] = 11[16 + 21(-5)] = 11[16 - 105] = 11[-89] = -979.

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