Progressions

The number of common terms in the two sequences 17, 21, 25, ..., 417 and 16, 21, 26, ..., 466 is

  1. 19
  2. 20
  3. 77
  4. 78

Answer

Total number of terms in the sequence 17, 21, 25 …417 is 101

Total number of terms in the sequence 16, 21, 26 …466 is 91

nth term of the first sequence = 4n + 13

mth term of the second sequence = 5m + 11

4n + 13 = 5m + 11

5m - 4n = 2

Possible integral values of n that satisfy 5m = 2 + 4n are (2, 7, 12 …97)

The total number of terms common in both the sequences is 20.

The correct option is B.