Answer
The ninth term of the sequence equals 6.
Work Step by Step
The general equation for the nth term of a geometric sequence is $a_n = a(r)^{n-1}$ where a = the first term and r = the common ratio. Since r is given as $\frac{1}{2}$ and a is given as 1536 plug these into the equation to get $a_n = 1536(\frac{1}{2})^{n-1}$. To find which number term of the sequence = 6 set the equation equal to 6 and solve for n: 6 = $1536(\frac{1}{2})^{n-1}$
1. To solve: Divide each side by 1536: .00390625 = $\frac{1}{2}^{n-1}$
2. Take the log base .5 of each side to further isolate n: 8 = n-1
3. n =9
The 9th term of the sequence equals 6.
