Multiple choice

Find the $n^{th}$ term of the sequence $m -1, m - 3, m - 5,.....$

  1. $m - n + 1$
  2. $m + 2n + 1$
  3. $m - 2n + 1$
  4. $m - 2n$
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C Correct answer
Explanation

This is an arithmetic progression with first term a = m-1 and common difference d = -2. The n-th term = a + (n-1)d = (m-1) + (n-1)(-2) = m - 1 - 2n + 2 = m - 2n + 1.

AI explanation

The sequence is an arithmetic progression where the first term a is m - 1 and the common difference d is -2. Using the formula for the nth term, Tn = a + (n - 1)d, we substitute the values to get Tn = (m - 1) + (n - 1)(-2). Simplifying this gives Tn = m - 1 - 2n + 2, which results in m - 2n + 1.

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