Question

Please help!!

A recursive rule for a geometric sequence is a1=4/9; an = 3a n−1.

What is the explicit rule for this sequence?


an=

Answer 1

The first term is given to be a1 = 4/9
The common ratio is 3 since we multiply each term by 3 to get the next term. This is shown in the formula a(n) = 3*a(n-1), which is the recursive step.

In other words,
nth term = 3*((n-1)st term)
next term = 3*(previous term)

So the rule for this sequence is

`a_(n) = (4)/(9)*\left(3\right)^(n-1)`
Note: if the image isn't showing then it says a(n) = (4/9)*(3)^(n-1)

Another note: the general nth term rule is a(n) = a1*(r)^(n-1)