Multiple choice

The number of common terms in the two sequences 17, 21, 25, __, 817 and 16, 21, 26, __, 851 is

  1. 28

  2. 39

  3. 40

  4. 87
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sequence 1: 17, 21, 25, ..., 817 (a=17, d=4). Sequence 2: 16, 21, 26, ..., 851 (a=16, d=5). Common terms start at 21 and increase by LCM(4,5) = 20. Common sequence: 21, 41, ..., up to 817. 817 = 21 + (n-1)20. 796 = (n-1)20. 39.8 = n-1, so n = 40.

AI explanation

The first common term is 21, and the common difference is the least common multiple of 4 and 5, which is 20. This forms an arithmetic progression of common terms: 21, 41, 61, and so on. Using the formula for the nth term, 21 + 20(n - 1) <= 817 yields 20(n - 1) <= 796, meaning n - 1 <= 39.8, resulting in 40 common terms.

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