The first term of a sequence is 2. After the first term, each term in the sequence is -1/2 term. What is the fifth term in the sequence?
The fifth term in the sequence is 1/8.
Starting with the first term as 2, each subsequent term is calculated by multiplying the previous term by -1/2. This leads to a predictable pattern that allows us to compute the fifth term effectively.
Calculating the sequence, the first term is 2, the second term is -1 (2 * -1/2), the third term is 0.5 (-1 * -1/2), the fourth term is -0.25 (0.5 * -1/2), and the fifth term is 1/8 (-0.25 * -1/2). Therefore, -0.03125 is not a term in the sequence.
Continuing the calculations, after obtaining the fourth term as -0.25, the fifth term, calculated as -0.25 * -1/2, results in 1/8. Since -0.0625 does not match this value, it is not the correct fifth term.
Following the sequence correctly, we find that the first term is 2, the second term is -1, the third term is 0.5, the fourth term is -0.25, and the fifth term, calculated as -0.25 * -1/2, is indeed 1/8. This aligns with our calculations and confirms this as the correct answer.
In the sequence, the terms decrease in magnitude and alternate in sign. As calculated, the fifth term is 1/8, which is far less than 1.4. Thus, this option does not fit within the established sequence.
The fifth term in the sequence, computed through consistent application of the recursive formula, is 1/8. Each term is derived by multiplying the previous term by -1/2, resulting in a sequence that alternates signs and reduces in value. The other choices do not align with this pattern, affirming 1/8 as the only valid answer.
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