Multiple choice

The two sequences 11, 16, 21, 26, ..., 211 and 10, 16, 22, 28, ..., 226 have how many terms in common?

  1. 6

  2. 7

  3. 8

  4. 9
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Sequence 1: 11, 16, 21, ..., 211 (a=11, d=5). Sequence 2: 10, 16, 22, ..., 226 (a=10, d=6). Common terms: 16 is the first. Next common term is 16 + LCM(5,6) = 16 + 30 = 46. Terms are 16, 46, 76, 106, 136, 166, 196. Total 7 terms.

AI explanation

The first arithmetic progression has a first term of 11 and a common difference of 5, meaning its general term is 11 + 5m. The second progression has a first term of 10 and a common difference of 6, making its general term 10 + 6k. Equating the two gives 1 + 5m = 6k, which means the common terms form a new sequence starting at 16 with a common difference equal to the least common multiple of 5 and 6, which is 30. The common terms are 16, 46, 76, 106, 136, 166, and 196, giving a total of 7 terms within both given ranges.

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