Step 1 Fora sequence to be arithmetic sequence difference between consecutive terms must be equal.

Mathematically,

\(d=t_{2}-t_{1}=t_{3}-t_{2}\)

Consider the given sequence: 9,13,17,21,...

Step 2

Now check for common difference,

\(d = 13 - 9 = 4\)

\(d = 17 - 13 = 4\)

This proves that,

\(4 = t_{2} - t_{1} = t_{3} -t_{2}\)

Therefore, it is arithmetic progression with common difference 4,