the second term in a geometric sequence is 12 the forth term in the same sequence is 4/3. what is the common ratio in this sequence

Question

terenzreignz · Answer

In a geometric sequence, each term is the previous term multiplied by a constant known as the common ratio.

Now, if the common ratio is r, and the second term is 12, what is the third term?

anonymous · Answer

the third term is 12r?

terenzreignz · Answer

That's right, and the fourth term is...?

terenzreignz · Answer

I know it's 4/3, but what is it in terms of the second term (12) and r?

anonymous · Answer

12r^2?

terenzreignz · Answer

That's correct ^_^
So the fourth term is $12r^2$ but you also know it to be $\Large \frac43$

Then
$$\Large 12r^2 = \frac43$$
You may now simply solve for r.

anonymous · Answer

thank you!

terenzreignz · Answer

No problem... though you can thank me by posting your answer :P

anonymous · Answer

.33?

terenzreignz · Answer

I prefer $\Large \frac13$
But you're correct ^_^

anonymous · Answer

care to help me with another one? :)

terenzreignz · Answer

Let's see it...

anonymous · Answer

the original value of a car is 18000$ and it depreciates by 15% each year. What is the value of the car after three years?

terenzreignz · Answer

Ahh... word problems... trust me, solving these things is usually easy (almost child's play) but then again, the tricky part is setting up EXACTLY WHAT TO SOLVE...

What are your ideas? ^_^

anonymous · Answer

well im looking for the 3rd term in a sequence?

terenzreignz · Answer

Yeah, I know, but how do you plan to solve this?

anonymous · Answer

by using the first equation you gave me?

terenzreignz · Answer

In this context, you can probably expect a geometric sequence to be involved...

terenzreignz · Answer

Okay, a good place to start would be to seek a common ratio... if you slash 15% off something, what remains?

anonymous · Answer

youd have 15300

terenzreignz · Answer

LOL,  I meant in general, if you slash 15% off of something, you get 85% remaining right?

anonymous · Answer

oh yeah lmao but would the answer be 11054.25?

terenzreignz · Answer

I actually don't know.
But what I meant is that when you slash off 15% of something, it's the same as multiplying it by 85% or 0.85 right?

anonymous · Answer

yeah it is

terenzreignz · Answer

So every year, you multiply it by 0.85, and three years have passed... so how many times do you multiply the original price by 0.85?

anonymous · Answer

three times

terenzreignz · Answer

You see where the concept of a geometric sequence plays in, you can consider 0.85 as the common ratio...

terenzreignz · Answer

So, the answer, is after three years, the new value is
$$\Large 18000\times 0.85^3$$

anonymous · Answer

and that gives you the answer that i previously stated, Thank you very much!! i wanted to check if i was correct :)

terenzreignz · Answer

I had to make sure YOU knew how to do it in general... say, if we change the discount, of if it were 10 years or something :P

anonymous · Answer

$$18000*.85^{10}$$

terenzreignz · Answer

LOL yeah :)
What if it were 10 years, but a 12% discount instead of 15% ?

anonymous · Answer

$$18000*.88^{10}$$

terenzreignz · Answer

You seem to have mastered it already XD

terenzreignz · Answer

Good job ^_^