consider a sequence whose first five terms are 64, 48, 36, 27, 20.25. select the function (with domain of all integers n greater than but equal to 1) that can be used to define and continue this sequence

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 :

Therefore , its an geometric progression with common ratio and first term is A = 64 .

General equation of G.P with common ratio r and first term A is :

Therefore , general equation sequence is given by :

Hence , this is the required solution .