Multiple choice

The first term of a sequence of numbers is $-3$. Each term after the first is obtained by multiplying the preceding term by $-1$ and then subtracting $1$. What is the $75^{th}$ term of the sequence?

  1. $-73$
  2. $-3$
  3. $2$
  4. $4$
  5. $73$
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B Correct answer
Explanation

The sequence is defined by a_1 = -3 and a_(n+1) = -a_n - 1. Calculating the first few terms: a_1 = -3, a_2 = -(-3) - 1 = 2, a_3 = -(2) - 1 = -3, a_4 = -(-3) - 1 = 2. The sequence alternates between -3 and 2, where odd-indexed terms are -3 and even-indexed terms are 2.

AI explanation

Using the given rule, the sequence begins -3, 2, -3, 2, and continues to alternate between these two numbers. Because all odd terms are -3 and even terms are 2, the 75th term corresponds to the odd positions. Therefore, the 75th term is -3.

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