Does the difference between any two consecutive terms always have the same value?
It is not an arithmetic sequence.
Practice makes perfect
We want to determine whether the sequence is an arithmetic sequence and, if so, write its recursive rule and explicit rule. Let's pay close attention to the difference between two consecutive terms.
128-64 ⟶64-32 ⟶32-16 ⟶16...
We can see that the difference between two consecutive terms is not always the same. Therefore, the given sequence is not an arithmetic sequence.
Extra
Looking for a Pattern
From the sequence we can see that, after the first term, each term is equal to the previous term divided by 2.
128 ÷ 2 ⟶ 64 ÷ 2 ⟶ 32 ÷ 2 ⟶ 16
Remember that dividing by 2 is the same as multiplying by 12.
128 * 12 ⟶ 64 * 12 ⟶ 32 * 12 ⟶ 16
A sequence where each term is multiplied by the same number to get the next term is called a geometric sequence.
