Given the geometric sequence: #4,24,144, ...#. What is the common ratio?

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Answer 1 · 2017-01-06T08:18:57

the common ratio is 6

The common ratio is obtained by calculating #a_(n+1)/a_n#

that's

#24/4=144/24=864/144=6#

Answer 2 · 2017-01-06T08:28:19

6

The #n^(th)# term of a geometric sequence is generated by:

#a_n = a_"n-1" xx r#
Where r is the common ratio

In this example: #a_0 = 4#

#a_1 = 24 = a_0 xx 6#

#a_2 = 144 = a_1 xx 6#

.. and similarly for #a_3#

Hence: The common ratio #r = 6#