4,9,14,19,24
A sequence is arithmetic when its terms continually increase or decrease by the same number called as the common difference.
So, let's find the common difference,
a_2-a_1=9-4=5
a_3-a_2=14-9=5
a_4-a_3=19-14=5
a_5-a_4=24-19=5
So the terms are increasing by the common difference of 5 which shows that the sequence is arithmetic.
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