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For x > 0, which term is the first one with a negative sign in the expansion of (1 + x)^(27/5)?

1. 6th term
2. 7th term
3. 5th term
4. 8th term

Correct answer: 8th term

Solution

In the binomial expansion of (1 + x)^(27/5), the terms alternate in sign based on the binomial coefficient and the power of x. The first negative term occurs when the exponent of x is odd, which happens at the 8th term, as the terms are indexed starting from zero.

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