Multiple choice

Find the sum of the series to $30$ terms: $1 - 50 + 4 - 45 + 7 - 40 +$ ...

  1. $-945$
  2. $105$
  3. $945$
  4. $1605$
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B Correct answer
Explanation

The series is (1+4+7+...) + (-50-45-40-...). There are 15 terms in each arithmetic progression. Sum 1 = (15/2)(2*1 + 14*3) = 7.5 * 44 = 330. Sum 2 = (15/2)(2*-50 + 14*5) = 7.5 * (-30) = -225. Total sum = 330 - 225 = 105.

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