Florida Teacher Certification Examinations (FTCE) Subject Area Practice Test 2026 - Free Practice Questions and Study Guide

To determine the 8th term of a geometric sequence, it is essential to identify the common ratio. In this sequence, the first term is -9, and each subsequent term is obtained by multiplying the previous term by the common ratio.

To find the common ratio, divide the second term by the first term:

36 ÷ -9 = -4.

Thus, the common ratio is -4. This means each term is -4 times the previous term.

Now, we can calculate the 8th term of the sequence. The nth term in a geometric sequence can be found using the formula:

\[

a_n = a_1 \cdot r^{(n-1)}

\]

where \(a_n\) is the nth term, \(a_1\) is the first term, \(r\) is the common ratio, and \(n\) is the term number.

For this sequence:

- First term (\(a_1\)) = -9

- Common ratio (\(r\)) = -4

- Term number (\(n\)) = 8

Substituting these values into the formula gives:

\[

a_8 = -9 \cdot (-4