Multiple choice

If $m$th terms of the series $63+65+67+69+.....$ and $3+10+17+24+....$ be equal, then $m=$

  1. $11$
  2. $12$
  3. $13$
  4. $15$
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C Correct answer
Explanation

Series 1: 63, 65, 67... (a=63, d=2). m-th term = 63 + (m-1)2 = 61 + 2m. Series 2: 3, 10, 17... (a=3, d=7). m-th term = 3 + (m-1)7 = 7m - 4. Equating: 61 + 2m = 7m - 4 => 65 = 5m => m = 13.

AI explanation

The mth term of the first arithmetic progression is 63 + (m - 1)2, and the mth term of the second arithmetic progression is 3 + (m - 1)7. Setting these two expressions equal gives the equation 63 + 2m - 2 = 3 + 7m - 7. Simplifying this yields 61 + 2m = 7m - 4, and solving for m gives 5m = 65. Therefore, the value of m is 13.

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