Help I'm trying to find the 8th term of the geometric sequence when a3=4 and a5=9

So I set up a system of two equations to find the common ratio which my answer says its square root of 5

a3=4 = a1 * r^2
a5=9 = a1* r^4

My problem is when I check to see if square root of 5 is the common I get a3=4 and a5=20. Is my common ratio off?

Question

Help I'm trying to find the 8th term of the geometric sequence when a3=4 and a5=9 

So I set up a system of two equations to find the common ratio which my answer says its square root of 5

a3=4 = a1 * r^2
a5=9 = a1* r^4

My problem is when I check to see if square root of 5 is the common I get a3=4 and a5=20. Is my common ratio off?

anonymous · Answer

It is.

anonymous · Answer

I thikn what you did was you took the difference of 4 and 9, and not their quotient.

anonymous · Answer

If it was an arithmetic series, you'd be correct in doing that, and then divide 5 by 2 to get a common DIFFERENCE of 2.5. But this is a geometric series. So you take their ratio, 9/4, take the square root (since they're a3 and a5, which differ by two - if they were a10 and a14, for example, you'd take the 4th root). Now, once you have a common ratio of $$\sqrt5$$, use that to find any term you need.

anonymous · Answer

yeah  that's what happened. Thanks for pointing that out