How are the consecutive terms related to each other?
Arithmetic or Geometric? Geometric sequence. Rule for the nth term: a_n=32( 12)^(n-1)
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 ratio of 12. We also see that the first term is 32. Therefore, the given sequence is a geometric sequence with first term a_1= 32 and common ratio r= 0.5 or r= 12. We can write its rule by substituting these values into the general rule for geometric sequences.
a_n=a_1r^(n-1) ⇒ a_n= 32( 1/2)^(n-1)
