Multiple choice

How many terms are common in the two sequences 9, 17, 25, 33 . . . (80 terms) and 11, 23, 35, 47 . . . (100 terms)

  1. 0

  2. 17

  3. 18

  4. 19

  5. None of these
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A Correct answer
Explanation

Sequence 1: 9, 17, 25, 33... (a=9, d=8). Sequence 2: 11, 23, 35, 47... (a=11, d=12). Common terms satisfy 9 + 8(n-1) = 11 + 12(m-1), which simplifies to 8n + 1 = 12m - 1, or 8n - 12m = -2, or 2n - 3m = -0.5. Since n and m must be integers, there are no common terms.

AI explanation

The general term for the first sequence is 8n plus 1, and the general term for the second sequence is 12m minus 1. Setting them equal gives 8n plus 1 equals 12m minus 1, which simplifies to 2n plus 1 equals 3m. Since the left side is always odd and the right side is always even, there are no integer solutions and no common terms exist.

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