How are the consecutive terms related to each other?
Arithmetic or Geometric Sequence? Arithmetic sequence. Rule for the nth term: a_n=- 3n+20
Practice makes perfect
We want to write a rule for the sequence given by the graph.
Let's organize the given points in a table, and pay close attention to how the consecutive terms are related to each other.
We can see that the consecutive terms have a common difference of -3. We also see that the first term is 17. Therefore, the given sequence is an arithmetic sequence with first term a_1= 17 and common difference d= - 3. We can write its rule by substituting these values into the general rule for arithmetic sequences.
