Question

Find the 5th term from the end of the G.P. `1/512, 1/256, 1/128`, ...256.

Answer 1

a = `1/512`

r = `1/256 xx 512`

r = `512/256`

r = 2

`a_n = ar^(n - 1)`

`256 = 1/512(2)^(n - 1)`

`256 xx 512 = 2^(n - 1)`

`2^(n - 1) = 2^8 xx 2^9`

`2^(n - 1) = 2^17`

n − 1 = 17

n = 17 + 1

n = 18

`a_n = ar^(14 - 1)`

= ar¹³

= `1/512(2)^13`

= `(2)^13/(2)^9`

= `2^(13 - 9)`

= 2⁴

= 16