Multiple choice

What is the sum of the first forty terms of the arithmetic sequence 120, 115, 110, 105....?

  1. 900

  2. 700

  3. 500

  4. 300
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A Correct answer
Explanation

Arithmetic sequence: a = 120, d = -5, n = 40. Sum = (n/2) * [2a + (n-1)d] = 20 * [240 + 39 * (-5)] = 20 * [240 - 195] = 20 * 45 = 900.

AI explanation

The given sequence is an arithmetic progression with a first term of 120 and a common difference of -5. Using the arithmetic series sum formula S = n/2 * [2a + (n-1)d], we substitute the known values to get S = 40/2 * [2(120) + (40-1)(-5)]. This simplifies to 20 * (240 - 195), which equals 20 * 45. The final sum of the first forty terms is 900.

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