Question

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

Answer 1

Total number of terms in the sequence 17,21,25 … 417 is equal to $\frac{417-17}{4}+1=101$
Total number of terms in the sequence 16, 21, 26 … 466 is equal to $\frac{466-16}{5}+1=91$
Nth term of the first sequence = 4n + 13.
Mth term of the second sequence = 5m +11.
As per the information given in the question 4n + 13 = 5m +11 $\Rightarrow$ 5m – 4n =2.
Possible integral values of n that satisfy 5m = 2+ 4n are (2, 7, 12 …97)
Therefore, the total number of terms common in both the sequences is 20.