Multiple choice

The first and last terms of an arithmetic progression are 37 and - 18. If the sum of the series is 114, then how many terms does it have?

  1. 13

  2. 12

  3. 14

  4. 15
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B Correct answer
Explanation

Sum = n/2 * (a + l). 114 = n/2 * (37 - 18) = n/2 * 19. 114 = 9.5n. n = 114 / 9.5 = 12.

AI explanation

The sum of an arithmetic progression is found using the formula S = n/2 * (first term + last term). Substituting the given values results in the equation 114 = n/2 * (37 - 18). This simplifies to 114 = n/2 * 19, which becomes 228 = 19n. Dividing 228 by 19 gives n = 12, meaning there are 12 terms in the series.

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