Multiple choice

Find the sum of the series $3+7+14+24+37+ ...... $up to $10$ terms.

  1. $570$
  2. $750$
  3. $705$
  4. $507$
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A Correct answer
Explanation

The differences between consecutive terms of the series are 4, 7, 10, 13, which form an arithmetic progression with a first term of 4 and a common difference of 3. The general term of the series is a_n = 1.5*n^2 - 0.5*n + 2. Summing this expression from n = 1 to 10 yields 1.5*385 - 0.5*55 + 20 = 570.

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