How do you tell whether the sequence #100, 50, 25, 25/2, 25/4,...# is geometric?

1 Answer
Oct 31, 2017

Answer:

The sequence is geometric with first term #a_1=100# and common ratio #r=0.5#

Explanation:

#a_1=100, a_2=50, a_3=25,a_4 = 25/2,a_5=25/4...#

#50/100=0.5 , 25/50=0.5 , (25/2)/25=0.5, (25/4)/(25/2)=0.5#

#:.a_2/a_1=a_3/a_2=a_4/a_3=a_5/a_4= 0.5#

The ratio of successive term and preceeding term is constant

#(r=0.5)# . Therefore the sequence is geometric whose first

term is #a_1=100# and common ratio is #r=0.5# [Ans]