## anonymous one year ago I need help on my Arithmetic and Geometric Sequence worksheet -24,-8,-2 2/3, -8/9 8,-4,2,-1 3/4,-1/2,1/3,-2/9 Find the next three terms

1. whpalmer4

Okay, do you know what an arithmetic sequence is, and a geometric sequence?

2. anonymous

Arithmetic is subtracting? Geometric is multiplying

3. whpalmer4

arithmetic is adding or subtracting, yes, and geometric is multiplying (or dividing) An arithmetic sequence always has the same difference between two adjacent terms, and a geometric sequence always has the same quotient between two adjacent terms. So are these arithmetic or geometric sequences?

4. anonymous

Geometric sequence?

5. whpalmer4

Yes, all 3 are geometric sequences. Can you work out what the ratio is for the first one? $-24,-8,-2\frac{2}{3},-\frac{8}{9}$

6. whpalmer4

$\frac{-24}{-8}=$$\frac{-8}{-2\frac{2}{3}}=$$\frac{-2\frac{2}{3}}{-\frac{8}{9}}=$

7. anonymous

They all equal to 3

8. whpalmer4

Each number in the sequence is 1/3 of the previous one, isn't it? $-24*\frac{1}{3} = -8$$-8*\frac{1}{3}=-\frac{8}{3} \ (=-2\frac{2}{3})$$-\frac{8}{3}*\frac{1}{3} = -\frac{8}{9}$

9. whpalmer4

so what is the term after $$-\dfrac{8}{9}$$ going to be?

10. anonymous

-8/27

11. whpalmer4

that's right! Here are the first 10 terms of that sequence: $\left\{-24,-8,-\frac{8}{3},-\frac{8}{9},-\frac{8}{27},-\frac{8}{81},-\frac{8}{243},-\frac{8}{729},-\frac{8}{2187},-\frac{8}{6561}\right\}$

12. whpalmer4

Now how about the next problem? $8,-4,2,-1$ What is the common ratio between the terms?

13. anonymous

Well the pattern is positive, negative, positive, negative. But the ratio is ... I don't know

14. anonymous

Is it -2?

15. whpalmer4

$\frac{8}{-4} = -2$$\frac{-4}{2} = -2$$\frac{2}{-1} = -2$ Looks like we divide by $$-2$$ to get the next term...

16. whpalmer4

That makes the next term in the sequence = ???

17. anonymous

So the next 3 terms would be .5 , -.25, .125

18. whpalmer4

Yep. Probably a bit clearer if you keep them as fractions rather than decimals. $8,-4,2,-1,1/2,-1/4,1/8$

19. whpalmer4

20. anonymous

$\frac{ 3 }{ 4 } ,-\frac{ 1 }{ 2 },\frac{ 1 }{ 3 },-\frac{ 2 }{ 9 }$

21. whpalmer4

Looking back at the problem, it's a little bit ambiguous as to whether we need to find the next term in each sequence, or the next 3 terms in each sequence. Probably safer to do the next 3 terms!

22. anonymous

I got it!!! its $\frac{ 1 }{ 1 }$ thats how i find the next 3 terms?

23. anonymous

Nevermind

24. anonymous

I'm stuck on the last one

25. whpalmer4

$\frac{3}{4}*\frac{a}{b} = -\frac{1}{2}$ can you find a fraction that makes that work?

26. whpalmer4

don't worry about the negative sign, you can just put that on afterward $\frac{3}{4}*\frac{a}{b} = \frac{1}{2}$ maybe start by multiplying everything by 4 $4*\frac{3}{4}*\frac{a}{b} = 4*\frac{1}{2}$$3*\frac{a}{b} = 2$$\frac{a}{b} = \frac{2}{3}$ so we get the next term by multiplying by $$-\dfrac{2}{3}$$ Let's check that: we start with \frac{3}{4}: $\frac{3}{4}*-\frac{2}{3} = -\frac{3*2}{4*3} = -\frac{1}{2}\checkmark$ $-\frac{1}{2}*-\frac{2}{3} = \frac{1*2}{2*3} = \frac{1}{3}\checkmark$ looks like that is the right multiplier...

27. anonymous

Yesss

28. anonymous

Thank you for helping me!! :)

29. whpalmer4

Hopefully these will all be easy for you now! As I mentioned earlier, you might want to play it safe and figure out the next 3 terms for each of the sequences. If it turns out you didn't need to, well, you got some practice.

30. anonymous

True that