How do you write a geometric sequence with a common ratio of 2/3?

1 Answer
Oct 24, 2016

Answer:

Geometric sequence is #{a_1,2/3a_1,4/9a_1,8/27a_1,....,(2/3)^(n-1)a_1}#

Explanation:

Common ratio of #2/3# means that a succeeding number is #2/3# times the preceding number.

Here if the first number of the geometric sequence is #a_1#,

second number #a_2# is #a_1xx2/3#

third number is given by #a_3=a_1xx(2/3)^2#

and #n^(th)# number is #a_n=a_1xx(2/3)^(n-1)#

and geometric sequence is #{a_1,2/3a_1,4/9a_1,8/27a_1,....,(2/3)^(n-1)a_1}#