Florida Teacher Certification Examinations (FTCE) Subject Area Practice Test

What is the 8th term of the geometric sequence: -9, 36, -144, 576, -2304, 9216, -36864?

1. 172, 896

2. 147, 456

3. 128, 512

4. 99, 461

The correct answer is: 147, 456

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