Which term of a series 1/4, -1/2, 1… is -128?
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9th
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10th
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11th
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12th
Reveal answer
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B
Correct answer
Explanation
This is a geometric progression with a = 1/4 and r = -2. The n-th term is a * r^(n-1). -128 = (1/4) * (-2)^(n-1). -512 = (-2)^(n-1). Since (-2)^9 = -512, n-1 = 9, so n = 10.
AI explanation
This sequence follows a geometric progression with the first term a = 1/4 and a common ratio r = -2. Using the formula for the nth term of a geometric progression, Tn = a * r^(n-1), we set Tn = -128. Solving the equation (1/4) * (-2)^(n-1) = -128 gives (-2)^(n-1) = -512. Since -512 equals (-2)^9, n - 1 = 9, which results in n = 10.