Question

Find the 4th term from the end of the G.P. `5/2, 15/8, 45/32, .... 10935/32768`

Answer 1

a = `5/2`

r = `15/(8(5))(2)`

r = `3/4`

`a_n = ar^(n - 1)`

`(5/2)(3/4)^(n - 1) = 10935/32768`

`(3/4)^(n - 1) = 10935/32768 xx 2/5`

`(3/4)^(n - 1) = 2187/16384`

`(3/4)^(n - 1) = (3/4)^7`

n − 1 = 7

n = 7 + 1

n = 8

a₅ = ar⁴

= `(5/2)(3/4)^4`

= `(5 xx 81)/(2 xx256)`

= `405/512`