Multiple choice

The sum to $200$ terms of the series $1+4+6+5+11+6+.....$ is

  1. $29,600$
  2. $29,800$
  3. $30,200$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The series is 1, 4, 6, 5, 11, 6... This is two interleaved series: (1, 6, 11, ...) and (4, 5, 6, ...). Each has 100 terms. Sum 1 = (100/2)(2*1 + 99*5) = 50(2+495) = 24850. Sum 2 = (100/2)(2*4 + 99*1) = 50(8+99) = 5350. Total = 24850 + 5350 = 30200.

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