Question

The First Term of a geometric sequence is 3,and The Third term is 4/3 find the fifth term?

Geometric Sequence

Answer 1

The fifth term is `u_5=16/27`

Explanation:

The terms of the GP are

The first term is `u_1=a=3`

The third term is `u_3=ar^2=4/3`

where the common ratio is `=r`

Therefore,

`u_3/u_1=(ar^2)/(a)=r^2=4/3*1/3=4/9`

Therefore,

The common ratio is `r=sqrt(4/9)=2/3`

The fifth term is

`u_5=ar^4=3*(2/3)^4=16/27`

Answer 2

See below

Explanation:

`a_3=a_1(r)^(3-1)`

`4/3=3r^2`

`4/9=r^2`

`r=+-2/3`

In our case it won’t matter if `r` is positive or negative, so let’s just use the positive `r`. Note: it would make a difference if you wanted to find any even term.

`a_5= 3(+-2/3)^(5-1)`

`a_5= 48/81= 16/27`