Question

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

Answer 1

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}`