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An AP has a positive first term and a negative common difference. Which statement about it is certainly true?

Class 10nth Term of an APAlgebra — Sequences
  • AThe terms keep decreasing, so from some term onwards every term is negative
  • BEvery term of the AP is negative
  • CThe terms keep increasing because the first term is positive
  • DThe AP must stop as soon as a term becomes negative

Step-by-Step Solution

With each term is smaller than the one before, so falls without limit and eventually goes below 0 and stays there. The first term is positive, so not every term is negative. Nothing forces the list to stop at the first negative term - an AP may continue for ever.
Answer: A) The terms keep decreasing, so from some term onwards every term is negative

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