Communities

Writing
Writing
Codidact Meta
Codidact Meta
The Great Outdoors
The Great Outdoors
Photography & Video
Photography & Video
Scientific Speculation
Scientific Speculation
Cooking
Cooking
Electrical Engineering
Electrical Engineering
Judaism
Judaism
Languages & Linguistics
Languages & Linguistics
Software Development
Software Development
Mathematics
Mathematics
Christianity
Christianity
Code Golf
Code Golf
Music
Music
Physics
Physics
Linux Systems
Linux Systems
Power Users
Power Users
Tabletop RPGs
Tabletop RPGs
Notifications
Mark all as read
Q&A

What's the common ratio for this geometric sequence?

+1
−0

Delayed learning some math, now I'm back at it.

Geometric sequences. Basically a sequence where it has a common ratio.

An example:

Sequence = {14, 28, 56, 112}
Ratio = 2
Proof = 14 * 2 * 2 * 2...

You can see where I'm going with this.

In my previous sequence question, I asked how I'm supposed to get the arithmetic means between two values. Here, I'm tasked to get geometric means this time. Getting geometric means is a lot more complicated because it requires multiplying and dividing instead.

So what are the values at the ends of the sequence? $16$ and $81$, and I have to find $3$ geometric means between them. My problem though is that I can't really use the same way I did with arithmetic sequences, so finding a common ratio is difficult.

Sequence = {16, ?, ?, ?, 81}
Ratio = ?
Proof = 16 * ? * ? * ? * ?...

Any ways of obtaining the common ratio of the sequence?

Why does this post require moderator attention?
You might want to add some details to your flag.
Why should this post be closed?

0 comment threads

1 answer

+2
−0

If you look at the first sequence and divide every term by 14, you get a much simpler sequence. Consider how you could find the ratio from this and try the method on the second sequence.

Further solution/hint

You can divide by the first term in the second sequence, too.

What remains is essentially a problem of type $$ r^4 = 81/16, $$ where $r$ is the unknown ratio.

Finally

From the previous we get $r = 3/2$. Repeated multiplication verifies that this is correct.

Why does this post require moderator attention?
You might want to add some details to your flag.

0 comment threads

Sign up to answer this question »

This community is part of the Codidact network. We have other communities too — take a look!

You can also join us in chat!

Want to advertise this community? Use our templates!

Like what we're doing? Support us! Donate