Answer :
Given :
First five terms of sequence are :
64, 48, 36, 27, 20.25
To Find :
Find a function of n can be used to define and continue this sequence .
Solution :
Ratio of two consecutive numbers :
[tex]\dfrac{48}{64}=\dfrac{3}{4}\\\\\dfrac{36}{48}=\dfrac{3}{4}\\\\\dfrac{27}{36}=\dfrac{3}{4}\\\\\dfrac{20.25}{27}=\dfrac{3}{4}[/tex]
Therefore , its an geometric progression with common ratio [tex]r=\dfrac{3}{4}[/tex] and first term is A = 64 .
General equation of G.P with common ratio r and first term A is :
[tex]a_n=Ar^{n-1}\\\\a_n=64\times (\dfrac{3}{4})^{n-1}[/tex]
Therefore , general equation sequence is given by :
[tex]a_n=64\times (\dfrac{3}{4})^{n-1}[/tex]
Hence , this is the required solution .