Multiple choice

The 10th common term between the series 3+7+11+... and 1+6+11+... is

  1. 191

  2. 193

  3. 211

  4. none of these
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A Correct answer
Explanation

Series 1: 3, 7, 11, 15... (a=3, d=4). Series 2: 1, 6, 11, 16... (a=1, d=5). Common terms: 11, 31, 51... (a=11, d=20). 10th term = a + 9d = 11 + 9*20 = 11 + 180 = 191.

AI explanation

The first common term of the two arithmetic progressions is 11, and the common difference of the sequence of common terms is the least common multiple of 4 and 5, which is 20. The formula for the nth common term is 11 + (n - 1)20. For the 10th common term, substituting 10 for n gives 11 + 9 * 20 = 11 + 180 = 191.

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