Multiple choice

The $10^{th}$ common term between series $3 +7+ 11+...$ and $1+ 6+ 11 ...$ is

  1. $191$
  2. $190$
  3. $192$
  4. $194$
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A Correct answer
Explanation

The first series is 3, 7, 11... (a=3, d=4). The second series is 1, 6, 11... (a=1, d=5). Common terms follow an arithmetic progression with the first term 11 and common difference LCM(4, 5) = 20. The 10th term is a + (n-1)d = 11 + (10-1)20 = 11 + 180 = 191.

AI explanation

The first common term between the two arithmetic progressions is 11. The common difference of the first series is 4 and the common difference of the second is 5, so the common difference for the common terms is the lowest common multiple of 4 and 5, which is 20. The 10th common term is found by adding 9 times 20 to the first term, giving 11 + 180, which equals 191.

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