Question

How do you find the next two terms of the geometric sequence `1/3, 5/6, 25/12,...`?

Answer 1

The next two terms are found by multiplying by the common ratio `r=5/2` which results in `125/24` and `625/48`.

Explanation:

A geometric sequence is a sequence of numbers generated by mutiplying the previous term by the common ratio or `r`.

Find the common ration `r` by dividing any term by the previous term.

In this example, `r= 5/6 -: 1/3 = 5/2`.

The second term is generated by multiplying the first term by `5/2`
or `1/3 * 5/2 = 5/6`

The third term is generated by multiplying the second term by `5/2` or `5/6 * 5/2= 25/12`

Similarly, the fourth term is `25/12 * 5/2 =125/24`

The fifth term is `125/24 *5/2 = 625/48`