first 5 terms in a sequence when a=5 and r=1/5

Question

Express in improper fraction

Answer 1

Given that first term a = 5

             and ratio r = 1/5

 The terms of the geometric series are in the form a, ar, ar^2, ar^3, ar^4, ar^5 .......................

 Where a is the first term and r is the common ratio.

First term t1 = a = 5

Second term t2 = ar = (5)(1/5)        

                                = 1

Third term t3= ar^2 = (5)(1/5)^2        

                                   =  (5)(1/25)

                                   = 5/25 = 1/5

 Fourth term t4= ar^3 = (5)(1/5)^3       

                                   =  (5)(1/125)

                                   = 5/125 = 1/25

Fifth term t5= ar^2 = (5)(1/5)^4       

                                   =  (5)(1/625)

                                   = 5/625 = 1/125

Therefore the first five terms of the series are 5, 1, 1/5, 1/25, 1/125.