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

1 Answer
Nov 4, 2016

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

Explanation:

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