How do you find the next two terms of the geometric sequence #405, 135, 45,...#?

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Answer 1 · 2016-11-04T16:51:02

The GP is #405, 135, 45, 15 ,5#

GP: #" "405, 135, 45, ?. ?#

You need to know what value the first term has been multiplied by to give the second term.
Is the same value multiplied by #T_2# to give #T_3#?

This value is called the common ratio (#r#).

#T_1 xx r rarr T_2" and " T_2 xx r rarr T_3#

#r = T_2/T_1" and "r = T_3/T_2#

#r = 135/405 = 1/3" and "r = 45/135 = 1/3#

[Note: # xx 1/3# is the same as #div 3#, but we always multiply in a G.P.]

#T_4 = 45xx1/3 = 15#

#T_5 = 15 xx 1/3 = 5#

The GP is #405, 135, 45, 15 ,5#