Question

What is the 9th term of the geometric sequence where a1 = -5 and a6 = -5,120? a. -327,680 b. -393,216 c. -458,752 d. -524,288

Answer 1

another simple formula but for geo seqs is\[a_n=a_1*r^{(n-1)}\]

Answer 2

we know a6 = a1*r^5; solving for r we get:

r = 5rt(a6/a1)

Answer 3

using this back in to find a9 we get:

a9 = a1*r^8

a9 = a1*[5rt(a6/a1)]^8

Answer 4

or we can just make all that an exponent

a9 = a1* (a6/a1)^(8/5)