Question

# Determine whether the sequence is arithmetic. If so, identify the common difference 1, 2, 4, 8, 16, …

Polynomial arithmetic
It is known that, a sequence is arithmetic when the differences between consecutive terms are the same. Calculate the difference between $$a_2\ and\ a_1$$
$$d_1 = a_2 - a_1 =2-1=1$$ Similarly $$d_2 = a_3 - a_2 =4-2=2$$ $$d_3 = a_4 - a_3 =8-4=4$$ $$d_4 = a_5 - a_4 =16-8=8$$ From above calculte the differences between each two terms is not common. So, the sequence is not arithmetic.