Exercise 15 Page 318

To write a recursive rule for the given sequence, we will use a table to organize the terms and find the pattern.

The sequence is geometric, with first term

a_{1} = 243

r = 0 . \overline{3},

or

\frac{1}{3} .

To write the recursive rule, we will substitute these values into the general formula for the recursive rule of a geometric sequence.

a_{1} = a a_{n} = r \cdot a_{n - 1} \Rightarrow a_{1} = 243 a_{n} = \frac{1}{3} a_{n - 1}