Question

What is the 9th term of the geometric sequence where a1 = –6 and a6 = –6,144?

Answer 1

a6 = a1 * q^5
-6.144 = -6 * q^5
q^5 = + 1024
q = sqrt 5 of 1024
q = sqrt 5 of 2^(10)
q = 2^ ( 10/5) =2^2 = 4 <--- important
a9 = a1 * q^8
a9 = -6 * 4^8

Answer 2

-393216=T9

a=-6

t6=-6144

-6144=a.r^n-1

-6144=-6 .r^5
1024=r^5

r=common ratio=4

t9=a.r^8

-393216

Answer 3

in gp for a next term tn=a*r^n-1

in Ap=a+(n-1)d