# Determine whether the given sequence is arithmetic. If so, then find the common difference. 80, 40, 20, 10, 5,...

Question
Polynomial arithmetic
Determine whether the given sequence is arithmetic. If so, then find the common difference. $$80, 40, 20, 10, 5,...$$

2020-11-13
Step 1 Given: The sequence, $$80, 40, 20, 10, 5,...$$ Step 2 To check it is arithmetic sequence, calculate the common difference $$d = a_2 - a_1$$
$$= 40 - 80$$
$$= -40$$
$$d = a_3 - a_2$$
$$= 20 - 40$$
$$= -20$$ Since, the common difference d is not same. The given sequence is not arithmetic.

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$$38, -22, -6, 10,...$$
$$d=?$$