Multiple choice

Number of identical terms in the sequences 2,5,8,11,…. upto 100 terms and 3,5,7,9,11,… upto 100 terms are

  1. 17

  2. 33

  3. 50

  4. 147
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B Correct answer
Explanation

Sequence 1: 2, 5, 8, 11... (a=2, d=3). Sequence 2: 3, 5, 7, 9, 11... (a=3, d=2). Common terms are 5, 11, 17... (a=5, d=6). The general term is 5 + (n-1)6 = 6n - 1. We need 6n - 1 <= 299 (the 100th term of seq 1 is 2 + 99*3 = 299). 6n <= 300, so n <= 50. However, the 100th term of seq 2 is 3 + 99*2 = 201. So 6n - 1 <= 201, 6n <= 202, n <= 33.66. There are 33 terms.

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