Multiple choice

Which term of the sequence $20, 19 \dfrac{1}{4}, 18 \dfrac{1}{2}, 17 \dfrac{3}{4}$,... is the first negative term ?

  1. 25

  2. 28

  3. 30

  4. 35
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Sequence: 20, 19.25, 18.5, 17.75... Arithmetic progression with a = 20, d = -0.75. We want a + (n-1)d < 0. 20 + (n-1)(-0.75) < 0. 20 < (n-1)(0.75). 26.66 < n-1. n > 27.66. The first integer n is 28.

AI explanation

The sequence is an arithmetic progression with the first term a = 20 and the common difference d = -0.75. Using the formula Tn = a + (n - 1)d, we find the first negative term by setting Tn less than 0, giving 20 + (n - 1)(-0.75) < 0. Solving this yields -0.75(n - 1) < -20, so n - 1 > 26.6 and n > 27.6; therefore, the first integer value for n is 28.

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