Multiple choice

Find the sum of the first 20 terms if the first term is -12 and the common difference is -5 in an arithmetic series.

  1. $-1190$
  2. $-1290$
  3. $-1390$
  4. $-1490$
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A Correct answer
Explanation

Sum = (n/2) * [2a + (n-1)d]. n = 20, a = -12, d = -5. Sum = (20/2) * [2(-12) + (19)(-5)] = 10 * [-24 - 95] = 10 * [-119] = -1190.

AI explanation

Using the arithmetic series sum formula S = n/2 * [2a + (n-1)d], we substitute the first term a = -12 and the common difference d = -5 for n = 20 terms. The calculation becomes S = 20/2 * [2(-12) + (20-1)(-5)], which simplifies to 10 * (-24 - 95). This results in 10 * -119, giving a total sum of -1190.

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