Help with two Geometric Sequence problems?

Question

anonymous · Answer

Given than a↓3 = 3, and a↓6 = -81, Find r.

anonymous · Answer

Given than a↓3 = 3, and a↓6 = -81, Find a↓1.

campbell_st · Answer

well formula for a term in an geometric series is 

$$a_{n} = a \times r^{n -1}$$

so in your questions you have 

$$a_{3} = 3 .. and... a_{6} = -81$$

so 

$$3 = ar^{3 -1}.... or... 3 = ar^2$$

$$-81 = ar^{6-1}.... or... -81= ar^5$$

you will solve the equation for r by substitution

$$-81 = ar^2 \times r^3$$

then 

$$-81 =3 \times r^3$$

now you can solve for r

hope this helps.

campbell_st · Answer

then you know r, substitute it into the 1st equation 

$$3 = ar^2$$

to find a

anonymous · Answer

a=3/r^2?

anonymous · Answer

I think the first one is 3

anonymous · Answer

And the second one is -1/3

anonymous · Answer

@some_someone @ryan123345

anonymous · Answer

$$r = \frac{ a _{n} }{ a _{n-1} }$$

anonymous · Answer

But what if I don't know what an is?

anonymous · Answer

well  @campbell_st preety much gave you all the info, such as setup so now just solve for what each thing says, what @campbell_st said.

anonymous · Answer

*pretty

anonymous · Answer

Oh ok, I know what to do now... Thanks!