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### Course: Operations and Algebraic Thinking 229+ > Unit 7

Lesson 3: Introduction to geometric sequences- Intro to geometric sequences
- Extending geometric sequences
- Extend geometric sequences
- Extend geometric sequences: negatives & fractions
- Using explicit formulas of geometric sequences
- Using recursive formulas of geometric sequences
- Use geometric sequence formulas

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# Extending geometric sequences

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

## Want to join the conversation?

- At0:13, why did he laugh? Did he say it wrong?(14 votes)
- because he said "sequenche" really funny apparently(33 votes)

- is there another way to explain this concept? So far, I've understood mostly everything except this?(4 votes)
- 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?(15 votes)

- is there a formula to figure out the common ration of a geometric sequence with fraction?(3 votes)
- 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, ...(17 votes)

- how do I know what to multiply by? like where did he get the -4 from?(2 votes)
- 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.(6 votes)

- What is the General rule used to find the nth term from Geometric Sequence?(2 votes)
- a(n) = a * r^(n-1) ... I hope the formating is not confusing(5 votes)

- In a geometric sequence would you ever divide to get to the next number in the sequence?(3 votes)
- Yes, the you could do multiplication or division and have a geometric sequence.(2 votes)

- 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.(5 votes)

- What is the recursive or explicit equation?(1 vote)
- how do I use the standard calculator times by 2/3(2 votes)
- type in *(2/3) and it should be right. Also, it's okay if you want to ignore the brackets in this case because times by 2/3 is the same thing as times 2 and divide by 3(2 votes)

- okay.. so to get the common ratio its a1 divided by a2?(0 votes)
- actually it's the 2nd term divided by the 1st term(6 votes)

## Video transcript

- [Voiceover] So we're told
that the first four terms of a geometric sequence are given. So they give us the first four terms. And they say what is the
fifth term in the sequence. And like always pause the video and see if you can come
up with the fifth term. Well what we have to remind ourselves is for a geometric sequence
each successive term is the previous term
multiplied by some number. And that number we call the common ratio. So let's think about it. To go from negative 1/32,
that's the first term to 1/8, what do we have to multiply by? What do we have to multiply by? Let's see. We're going to multiply, it's going to be multiplied by a negative since we went from a
negative to a positive. So we're going to multiply by negative and there's going to be a one over let's see to go from a 32 to an eight, actually it's not going to be a one over. It's going to be, this is
four times as large as that. It's going to be negative four. Negative 1/32 times negative
four is positive 1/8. Just to make that clear. Negative 1/32 times negative four that's the same thing
as times negative four over one. It's going to be positive. Negative times a negative is a positive. Positive four over 32. Which is equal to 1/8. Now let's see if that holds up. So to go from 1/8 to negative 1/2 we once again would
multiply by negative four. Negative four times 1/8 is negative 4/8, which is negative 1/2 and so then we multiply
by negative four again. So, let me make it clear. We're multiplying by
negative four each time. You multiply by negative four again, you get to positive two. Because negative four over negative two, you can do it that way, is positive two. And so to get the fifth
term in the sequence, we would multiply by negative four again. And so two times negative
four is negative eight. Negative four is the common ratio for this geometric sequence. But just to answer the question, What is the fifth term? It is going to be negative eight.