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

- 19
- 20
- 77
- 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

n^{th} term of the first sequence = 4n + 13

m^{th} 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.**