Step 1

For a sequence to be arithmetic sequence difference between consecutive terms must be equal.

Mathematically,

\(\displaystyle{d}={t}_{{{2}}}-{t}_{{{1}}}={t}_{{{3}}}-{t}_{{{2}}}\)

Consider the given secuence:

\(\displaystyle{9},\ {13},\ {17},\ {21},\ \cdots\)

Step 2

Now check for common difference,

\(\displaystyle{d}={13}-{9}={4}\)

\(\displaystyle{d}={17}-{13}={4}\)

This proves that,

\(\displaystyle{4}={t}_{{{2}}}-{t}_{{{1}}}={t}_{{{3}}}-{t}_{{{2}}}\)

Therefore, it is a arithmetic progression with common difference 4.

For a sequence to be arithmetic sequence difference between consecutive terms must be equal.

Mathematically,

\(\displaystyle{d}={t}_{{{2}}}-{t}_{{{1}}}={t}_{{{3}}}-{t}_{{{2}}}\)

Consider the given secuence:

\(\displaystyle{9},\ {13},\ {17},\ {21},\ \cdots\)

Step 2

Now check for common difference,

\(\displaystyle{d}={13}-{9}={4}\)

\(\displaystyle{d}={17}-{13}={4}\)

This proves that,

\(\displaystyle{4}={t}_{{{2}}}-{t}_{{{1}}}={t}_{{{3}}}-{t}_{{{2}}}\)

Therefore, it is a arithmetic progression with common difference 4.