We will find the first four terms of the described sequence, then graph them. After that, we will write a recursive and an explicit rule for the sequence.
Graph
We will make a table to show the first four terms. Note that the first term is 16 and the common ratio is 12.
Let's plot the ordered pairs (1,16), (2,8), (3,4), and (4,2).
Recursive Rule
The sequence a_n is a geometric sequence, with first term a_1=16 and common ratio r= 12. Now we can write the recursive equation.
a_n= r* a_(n-1) ⇒ a_n= 1/2* a_(n-1)
The recursive rule is the recursive equation together with the first term.
Recursive Rule: a_1=16, a_n=1/2* a_(n-1)
Explicit Rule
The explicit rule for a geometric sequence is the formula a_n=a_1(r)^(n-1), where a_1 is the first term and r is the common ratio. We know a_1= 16 and r= 12
Explicit Rule: a_n= 16( 1/2)^(n-1)
