Question

Number of terms common to the two sequences $17,21,25,...,417$ and $16,21,26,....,466$ is

• A. $19$
• B. $20$
• C. $21$
• D. $22$

Answer 1

The correct option is B $20$

Now, the total number of terms in the sequence $17,21,25\dots 417$ are $101$

Also, the total number of terms in the sequence $16,21,26\dots 466$ are $91$

The nth term of the first sequence $=4n+13$

The mth term of the second sequence $=5m+11$

Equating both the expressions, we have

$4n+13=5m+11$

Thus

$5m-4n=2$

Now, the possible integral values of n that satisfy $5m=2+4n$ are $(2,7,12\dots 97)$

Thus the total number of terms common in both the sequences is $20$