Question

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

Answer 1

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`