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

Geometric Sequence

2 Answers
Narad T.
Jul 25, 2018

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

Hriman
Jul 25, 2018

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

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