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#