QuestionFind an explicit formula for the $n^{\text {th }}$ term of this sequence. $$\begin{array}{l} 9,-1, \frac{1}{9},-\frac{1}{81}, . . \\ a_{n}= \end{array}$$

Studdy Solution
Write the explicit formula for the $n^{\text{th}}$ term of the sequence.
The formula for the $n^{\text{th}}$ term of a geometric sequence is given by:
$$a_n = a_1 \cdot r^{n-1}$$
Substitute the values of $a_1$ and $r$:
$$a_n = 9 \cdot \left(-\frac{1}{9}\right)^{n-1}$$
This is the explicit formula for the $n^{\text{th}}$ term of the sequence.
The explicit formula for the $n^{\text{th}}$ term is:
$$a_n = 9 \cdot \left(-\frac{1}{9}\right)^{n-1}$$