Question

5, _, 405 is a geometric sequence.. determine all possible values for the second term of this sequence.. determine all possible general terms for this sequence

Answer 1

Well my first thought was to do 405 ÷ 5 = x

Answer 2

no.. that's not it

Answer 3

wish it was that simple

Answer 4

Cool, thanks

Answer 5

the answer key says.. r=9 or -9

Answer 6

i am so confused

Answer 7

Geometric sequence states that the first term is a. The second term is ar, the 3rd is \[ar^{2}\], etc.

So if 5 is the first term, and 405 is the third term:
a = 5
\[ar^{2} = 405\]
substitute a = 5 into the 2nd equation and you get:
\[5r^{2} = 405\]
\[r^{2} = 81\]
r = +9, -9

Therefore, you have two possible geometric sequences:
5,-45,405,3645 where r = -9
5,45,405,3645 where r = +9