Question

The number of common terms of the sequence $17,21,25,.....,417$ and $16,21,26,.......,466$ is

• A. $21$
• B. $19$
• C. $20$
• D. None of these

Answer 1

The correct option is C

$20$

Explanation for the correct option:

Find the number of common terms in the given series.

Two series $17,21,25,.....,417$ and $16,21,26,.......,466$ is given.

It is clear that both the series are Arithmetic progression series with a common difference $4$ and $5$ respectively.

It is also clear that the first common term is $21$.

We know that the common difference of the arithmetic series of all the common terms is given by $4·5=20$.

Since the last common term will be smaller than $417$.

Therefore, the Arithmetic progression series of common terms is $21,41,61,.......,401$.

Compute the last of the series as follows.

$$\begin{gathered} 21+(n-1)20=401 \\ \Rightarrow (n-1)20=380 \\ \Rightarrow (n-1)=19 \\ \Rightarrow n=20 \end{gathered}$$

Therefore, the number of common terms in the given series is $20$.

Hence, option $C$ is the correct answer.