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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