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### Course: Algebra I (2018 edition)>Unit 8

Lesson 3: Introduction to geometric sequences

# Extending geometric sequences

Sal finds the next term in the geometric sequence -1/32, 1/8, -1/2, 2,...

## Want to join the conversation?

• At , why did he laugh? Did he say it wrong?
• because he said "sequenche" really funny apparently
• is there another way to explain this concept? So far, I've understood mostly everything except this?
• There maybe another way, but in order to help you, I need try to understand what you are having trouble with.

Have you watched the previous video, "Intro to geometric sequences"? Make sure you understand what geometric sequence is.

What is it that is confusing you in this video? Pause the video at the point where start to get lost, what time does it say on video progress line?
• is there a formula to figure out the common ration of a geometric sequence with fraction?
• To find the common ratio, you divide the next number by the current number. So lets say the common ratio is 1/2. a sequence starting from 32, 16, 8, 4, 2, 1, .5 ... You can divide starting anywhere, so 16/32 = 1/2, 8/16 = 1/2, 4/8 = 1/2, ...
• how do I know what to multiply by? like where did he get the -4 from?
• The common ratio is found by dividing consecutive terms (second divided by 1st), so (1/8)/(-1/32) = (1/8)*(-32)=-4. Or (-1/2)/(1/8)= -1/2*6=-4, this pattern continues 2/(-1/2) = 2*-3=-4. Each give a common ratio of -4. so next is (2)(-4)=-8, then -8*-4=32, etc.
• What is the General rule used to find the nth term from Geometric Sequence?
• a(n) = a * r^(n-1) ... I hope the formating is not confusing
• In a geometric sequence would you ever divide to get to the next number in the sequence?
• Yes, the you could do multiplication or division and have a geometric sequence.
• how to know what fraction I'm multiplying with, I'm not good at this
(1 vote)
• If you have two terms next to each other, for example F2 and F3 in the geometric sequence F, then you can simply divide F3 by F2 -> F3 / F2 to get the common ratio.
However if they are separated by a few terms, then this requires a little bit of thinking.
For example you are given F2 and F5, let the common ratio (Not found, but we simply let it be some unknown) be r.
Notice you can get F5 by multiplying F2 and multiple times of r. In this case, F2 * r * r * r = F5.
So you can perform some algebra and get the common ratio.
• What is the recursive or explicit equation?
(1 vote)
• how do I use the standard calculator times by 2/3