We will find the first four terms, 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. We know a_1=8 and r=5.
Let's plot the ordered pairs (1,8), (2,40), (3,200), and (4,1000).
Recursive Rule
The sequence a_n is a geometric sequence, with first term a_1=8 and common ratio r= 5. This allows us to write a recursive equation.
a_n= r* a_(n-1) ⇒ a_n= 5* a_(n-1)
The recursive rule is the recursive equation together with the first term.
Recursive Rule: a_1=8, a_n=5* 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= 8 and r= 5
Explicit Rule: a_n= 8( 5)^(n-1)
