Question

The first term of a geometric sequence is 5, and the third term is 16/5. How do you find the fifth term?

Answer 1

fifth term is `256/125`

Explanation:

For a geometric sequence
`color(white)("XXX")a_(i+1) = a_i*r` for `i > 1` and some constant `r`
`color(white)("XXX")a_(i+2) = a_i*r^2`

Given
`color(white)("XXX")a_1 = 5`
and
`color(white)("XXX")a_3=16/5`

`color(white)("XXX")=5*r^2`

`color(white)("XXX")r^2= 16/25`

`color(white)("XXX")r^4= (16^2)/(25^2)`

`color(white)("XXX")a_5 = a_1*r^4 = (cancel(5)*16^2)/(cancel(25)_5*25) = 256/125`