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

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Answer 1 · 2016-10-23T22:45:53

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

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 $125/24 *5/2 = 625/48$

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