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 $405, 135, 45, 15 ,5$

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