Multiple choice

How many terms of the sequence $18, 16, 14,....$ should be taken so that their sum is zero?

  1. $19$
  2. $17$
  3. $18$
  4. $16$
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A Correct answer
Explanation

Sum of arithmetic series = (n/2)[2a + (n-1)d]. Here a=18, d=-2. Sum = (n/2)[36 + (n-1)(-2)] = (n/2)[36 - 2n + 2] = (n/2)[38 - 2n] = n(19-n). For sum to be zero, n=19.

AI explanation

The given sequence is an arithmetic progression with the first term a = 18, common difference d = -2, and sum S_n = 0. Using the arithmetic series sum formula S_n = n/2 [2a + (n - 1)d], we substitute the values to get 0 = n/2 [36 + (n - 1)(-2)]. Simplifying this yields 0 = n/2 (38 - 2n), which further reduces to 2n = 38, so n = 19.

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