Question

What is the 9th term of the geometric sequence where a1 = -8 and a6 = -8,192

Answer 1

We can use the terms provided to find the common ratio of the geometric series. The nth term of a geometric series is given by \[a_n=ar^{n-1}\]where a is the initial value which is -8 in this particular case. We can use the a6 term to form the equation\[-8,192=-8r^{5}\] Dividing by -8 we get\[1024=r^5\] Taking the 5th root if 1024 we get\[r=\sqrt[5]{1024}=4\] So to find the ninth term we have\[a_9=(-8)4^8=-524,288\]

Answer 2

thanks