# Determine whether the given sequence is arithmetic. If so, then find the common difference. 4, 9, 14, 19, 24,...

Polynomial arithmetic
Determine whether the given sequence is arithmetic. If so, then find the common difference. $$4, 9, 14, 19, 24,...$$

2020-10-19
From the above sequence, it can be observed that $$a_1 = 4,a_2 =9,a_3 =14,a_4 =19,a_5 = 24.$$ Subtract the two consecutive numbers of the sequence as shown below: $$a_2 - a_1 =9-4$$
$$=5$$
$$a3 - a2 =14-9$$
$$=5$$
$$a_4 - a_3 =19-14$$
$$=5$$
$$a_5 - a_4 =24-19$$
$$=5$$ It can be seen that the difference between the two consecutive numbers of the sequence is 5 (a constant). Thus, the given sequence is arithmetic and the common difference is 5.