Multiple choice

$11$ the $p$th term of the series $25,22 \frac { 3 } { 4 } , 20 \frac { 1 } { 2 } , 18 \frac { 1 } { 4 } , \ldots$ is numerically the smallest, then $p =$ ________.

  1. $11$
  2. $12$
  3. $13$
  4. $14$
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A Correct answer
AI explanation

The series is an arithmetic progression where the first term is 25 and the common difference is -2.25. The pth term is given by Tp = 25 + (p - 1)(-2.25). Since the smallest term must be positive, we set 25 - 2.25(p - 1) > 0, which simplifies to 2.25(p - 1) < 25. Solving this yields p < 12.11, meaning the maximum integer value for p is 11.