Question

Find the 6th term from the end of the gp 8,4,2.....1/1024

Answer 1

a = 8
r = 4/8
r = 1/2

Formula for nth term in gp :
An = a*(r)^n
1/1024 = 8 * (1/2)^n
(1/2)^n = 1/(1024*8)
(1/2)^n = 1/8192
2^(-n) = 1/8192

But, 2^(13) = 8192
So, 2^(-13) = 1/8192

2^(-n) = 2^(-13)
Since base is the same , so the powers can be equated.
-n = -13
n = 13

So, 1/1024 is 13th term
Since the last term is 13th term the 6th term from end will be 8th term
So, by the formula ,
An = a*(r)^n
A8 = 8 * (1/2)^(8)
A8 = (2)^(3) * (2)^(-8)
A8 = (2)^(-5)
A8 = 1/32

So, the 6th term from the end is 1/32