Question

PLEASE HELP!!!! i REALLY NEED TO GET THIS DONE AND AM HAVING TROUBLE WITH THIS ONE!!!!
The explicit rule for a sequence is given

an = 1/2(4/3)^n−1

Enter the recursive rule for the geometric sequence

Answer 1

Answer:

a[n] = a[n-1]×(4/3)

a[1] = 1/2

Step-by-step explanation:

The terms of a geometric sequence have an initial term and a common ratio. The common ratio multiplies the previous term to get the next one. That sentence describes the recursive relation.

The general explicit term of a geometric sequence is ...

  a[n] = a[1]×r^(n-1) . . . . . where a[1] is the first term and r is the common ratio

Comparing this to the expression you are given, you see that ...

  a[1] = 1/2

  r = 4/3

(You also see that parenthses are missing around the exponent expression, n-1.)

A recursive rule is defined by two things:

1. the starting value(s) for the recursive relation
2. the recursive relation relating the next term to previous terms

The definition of a geometric sequence tells you the recursive relation is:

  the next term is the previous one multiplied by the common ratio.

In math terms, this looks like

  a[n] = a[n-1]×r

Using the value of r from above, this becomes ...

  a[n] = a[n-1]×(4/3)

Of course, the starting values are the same for the explicit rule and the recursive rule:

  a[1] = 1/2