Question

Find the 6th term from the end of the G.P. 16, 8, 4, 2, ....., 1/512.

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

Answer 2

HOLA MATE

✍️ANSWER:-

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